Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Nature of Mathematics (MindTap Course List)
26PS27PS28PSIn Problems 2438, classify each as a permutation, a combination, or neither, and then answer the question. A shipment of 100 TV sets is received. Six sets are to be chosen at random and tested for defects. In how many ways can six sets be chosen?In Problems 2438, classify each as a permutation, a combination, or neither, and then answer the question. A night watchman visits 125 offices every night. To prevent others from knowing when he will be at a particular office, he varies the order of his visits to these 125 offices. In how many ways can this be done?In Problems 2438, classify each as a permutation, a combination, or neither, and then answer the question. A certain manufacturing process calls for the mixing of six chemicals. One liquid is to be poured into the vat, and then the others are to be added in turn. All possibilities must be tested to see which gives the best results. How many tests are required?32PSIn Problems 2438, classify each as a permutation, a combination, or neither, and then answer the question. What is the number of distinguishable arrangements in the letters in the word KARL?34PS35PSA space shuttle mission consists of a commander, a pilot, 3 engineers, a doctor, a scientist, and a civilian. It there are 7 people from whom the commander and pilot must be chosen, 18 possible engineers, 4 possible doctors, 7 scientist and 3 candidates for the civilian crew member, in how many ways can a crew be formed?37PS38PS39PSConsider selecting two elements, say, a, and b, from the set A=a,b,c,d,e. List all possible subsets of A using both elements, as well as all possible arrangements.Consider selecting three elements, say, c,d, and e, from the set A=a,b,c,d,e. List all possible subsets of A using all three elements. How many arrangements are there?42PS43PS44PS45PS46PS47PS48PS49PS50PS51PS52PS54PS55PS56PS57PS58PS59PS60PS1PS2PS3PS4PS5PS6PS7PS8PS9PS10PS11PS12PS13PS14PS15PS16PS17PS18PS19PS20PS21PS22PS23PS24PS25PS26PS27PS28PS29PS30PS31PS32PSDetermine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle.34PSDetermine whether each of the figures in Problems 30-37 will be a solution to an Instant Insanity puzzle.36PS37PS38PS39PS40PS41PS42PS43PS44PS45PS46PS47PS48PS49PS50PS51PS52PS53PS54PS55PS56PS57PS58PS59PS60PS1CR2CR3CR4CR5CR6CR7CR8CR9CR10CR11CR12CRHow many distinguishable permutations are there of the letters of the words HAPPY and COLLEGE?14CR15CR16CRBob has one pair of shabby slacks, forty ties, seven shirts, and five sports jackets, but has absolutely no sense of style. In how many ways can Bob dress for the day?a.A certain mathematics test consists of 10 questions. In how many ways can the test be answered if the possible answers are true and false? b.Answer the question if the possible answers are true, false, and maybe. c.Answer the question if the possible answers are a, b, c, d, and e; that is, the test is multiple choice.19CR20CRIN YOUR OWN WORDS What is the difference between empirical and theoretical probabilities?IN YOUR OWN WORDS Define probabilities?3PS4PS5PS6PS7PS8PSGive the probabilities in Problems 9-11 in decimal form correct to two decimal places. A calculator may be helpful with these problems. Last year, 1,485 calculators were returned to the manufacturer. If 85,000 were produced, assign a number to specify the probability that a particular calculator would be returned.Give the probabilities in Problems 9-11 in decimal form correct to two decimal places. A calculator may be helpful with these problems. Last semester, a certain professor gave 13 As out of 285 grades. If one of the 285 students is to be selected at random what is the probability that his or her grade is an A?Give the probabilities in Problems 9-11 in decimal form correct to two decimal places. A calculator may be helpful with these problems. Last year in Ferndale, California, it rained on 75 days. What is the probability of rain on a day selected at random?12PSPoker is a common game in which players are dealt five cards from a deck of cards. In Example 4, Section 12.2, we found there are 2,598,960 different possible poker hands. The winning hands from highest to lowest are shown in Table13.1. Find the requested probabilities in Problems 13-17. Use a calculator, and show your answers to whatever accuracy possible on your calculator. Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3,744 hands Flush 5,108 hands Straight 10,200 hands Three of a kind 54,912 hands Two pair 123,552 hands One pair 1,098,240 hands Other hands 1,302,540 hands a. Proyal flush b. Pother straight flushPoker is a common game in which players are dealt five cards from a deck of cards. In Example 4, Section 12.2, we found there are 2,598,960 different possible poker hands. The winning hands from highest to lowest are shown in Table13.1. Find the requested probabilities in Problems 13-17. Use a calculator, and show your answers to whatever accuracy possible on your calculator. Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3,744 hands Flush 5,108 hands Straight 10,200 hands Three of a kind 54,912 hands Two pair 123,552 hands One pair 1,098,240 hands Other hands 1,302,540 hands a. Pfour of a kind b. Pfull housePoker is a common game in which players are dealt five cards from a deck of cards. In Example 4, Section 12.2, we found there are 2,598,960 different possible poker hands. The winning hands from highest to lowest are shown in Table13.1. Find the requested probabilities in Problems 13-17. Use a calculator, and show your answers to whatever accuracy possible on your calculator. Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3,744 hands Flush 5,108 hands Straight 10,200 hands Three of a kind 54,912 hands Two pair 123,552 hands One pair 1,098,240 hands Other hands 1,302,540 hands a. Pflush b. Pstraight16PS17PS18PS19PS20PS21PSSome numbers are shown in Table 13.1. Explain where the numbers in Problems 18-22 come from. The 5,108 hands called flush Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3,744 hands Flush 5,108 hands Straight 10,200 hands Three of a kind 54,912 hands Two pair 123,552 hands One pair 1,098,240 hands Other hands 1,302,540 handsa. One airline has six across seating in coach. If seats are assigned randomly, what is the probability that a person will be struck in a middle seat? b. Another airline has five across seating. If seats are assigned randomly, what is the probability that a person will have a window or an aisle seat?A single card is selected from an ordinary deck of cards. The sample space is shown in Figure 12.2. find the probabilities in Problems 24-27. a. P(fiveofclubs) b. P(five) c. P(club)A single card is selected from an ordinary deck of cards. The sample space is shown in Figure 12.2. find the probabilities in Problems 24-27. a. P(jack) b. P(spade) c. P(jackofspades)A single card is selected from an ordinary deck of cards. The sample space is shown in Figure 12.2. find the probabilities in Problems 24-27. a. P(fiveandajack) b. P(fiveandajack)A single card is selected from an ordinary deck of cards. The sample space is shown in Figure 12.2. find the probabilities in Problems 24-27. a. P(heartandajack) b. P(heartorajack)Suppose that you toss a coin and roll a die in Problems 28-31.the sample sapce is shown in Figure 13.1. What is the probability of obtaining: a. Tails and a five? c. Heads and a two? b. Tails or a five?29PSSuppose that you toss a coin and roll a die in Problems 28-31.the sample sapce is shown in Figure 13.1. What is the probability of obtaining: a. Heads and an odd numbers? b. Heads or an odd numbers?Suppose that you toss a coin and roll a die in Problems 28-31.the sample sapce is shown in Figure 13.1. What is the probability of obtaining: a. Heads and a five? b. Heads or a five?Use the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice. P(five).33PSUse the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice. P(seven).35PS36PSUse the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice. P(fourorfive).Use the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice. P(even).Use the sample space shown in Figure 13.5 to find the probabilities in Problems 32-39 for the experiment of rolling a pair of dice. P(eightorten).Suppose you and an opponent each pick one of the spinners shown here. Awin means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners given in Problems 40-47 you would choose in each case.. A plays B.Suppose you and an opponent each pick one of the spinners shown here. Awin means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners given in Problems 40-47 you would choose in each case.. A plays C.42PS43PSSuppose you and an opponent each pick one of the spinners shown here. Awin means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners given in Problems 40-47 you would choose in each case.. E plays F.45PS46PSSuppose you and an opponent each pick one of the spinners shown here. Awin means spinning a higher number. Construct a sample space to answer each question, and tell which of the two spinners given in Problems 40-47 you would choose in each case.. F plays C.Perform the experiments in Problems 48-51, tally your results, and calculate the probabilitites to the nearest hundredth. Toss a coin 100 times. Make sure that, each time the coin is flipped, it rotates several times in the air and lands on a table or on the floor. Keep a record of the results of this experiments. Based on your experiment, what is Pheads?.49PSPerform the experiments in Problems 48-51, tally your results, and calculate the probabilitites to the nearest hundredth. Flip three coins simultaneously 100 times, and not the results. The possible outcomes are: a. three heads b. two heads and one tail c. two tails and one head d. three tails Based on your experiment, find the probabilities of each of these events. Do these appear to be equally likely?Perform the experiments in Problems 48-51, tally your results, and calculate the probabilitites to the nearest hundredth. Simultaneously toss a coin and roll a die 100 times, and note the outcome of each trial. The possible outcomes are H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, and T6. Do these appear to be equally likely outcomes?52PSSuppose it is certain that an earthquake will occur some day. What is the probability to the nearest percent that it will occur while you are at school? Assume you are at school 5 hours per day, 174 days per year.Dice is a popular game in gambling casinos. Two dice are tossed, and various amounts are paid according to the outcome. If a seven or eleven occurs on the first roll, the player wins. a. What is the probability of winning on the first roll? b. The player loses if the outcome of the first roll is a two, three, or twelve. What is the probability of losing on the first roll?In dice, a pair of ones is called snake eyes. What is the probability of losing a dice game by rolling snake eyes?Consider a die with only four sides, marked one, two, three, and four. a. Write out a sample space simillar to the one in Figure 13.5 for rolling a pair of these dice. Assuming equally likely outcomes, find the probability that the sum of the dice is the given number. b. P(two) c. P(three) d. P(four) e. P(five) f. P(six) g. P(seven)The game of Dungeons and Dragons uses nonstandard dice. Consider a die with eight sides marked one, two, three, four, five, six, seven, and eight. Write a smaple space simillar to the one in Figure 13.5 for rolling a pair of these dice.A mad scientist has captured you and is showing you around his foul-smelling laboratory. lie motions to an opaque. formalin-filled jar. This jar contains one organ, either a kidney or a brain," he cheerily informs you. His voice seems an octave too high as he gives you a twisted leer. You watch as the mad-man grabs a brain lying on his worktable and drops it into the jar as well. He then shakes the jar and quickly withdraws a single organ. It proves to be a brain. He turns to you and says. "What is now the chance of removing another brain?" Fearing that the scientist might remove your brain in his next ghoulish experiment, you want to give him the right answer. What is your response?Level 1 IN YOUR OWN WORDS True or false? In roulette, if you bet on black, the probability of winning is 12 because there are equal numbers of black and red spots. Explain.Level 1 IN YOUR OWN WORDS True or false? An expected value of 5 means that you should expect to win 5 each time you play the game. Explain.3PS4PS5PS6PSLevel 1 Use estimation to select the best response in Problems 712. Do not calculate. The expectation from playing a game in which you win 950 by correctly calling heads or tails when you flip a coin is about A. 500 B. 50 C. 950Level 1 Use estimation to select the best response in Problems 712. Do not calculate. The expectation from playing a game in which you win 950 by correctly calling heads or tails on each of five flips of a coin is about A. 500 B. 50 C. 9509PSLevel 1 Use estimation to select the best response in Problems 712. Do not calculate. If your expected value when playing a 1 game of roulette is 0.05, then after playing the game 100 times you should have netted about A. 105 B. 5 C. 5Level 1 Use estimation to select the best response in Problems 712. Do not calculate. The probability of correctly guessing a telephone number is about A. 1 out of 100 B. 1 out of 1,000 C. 1 out of 1,000,000Level 1 Use estimation to select the best response in Problems 712. Do not calculate. Winning over 10 million in a super lottery is about as probable as A. having a car accident B. having an item fall out of the sky into your yard C. being a contestant on JeopardyLevel 1 Suppose that you roll two dice. You will be paid 5 if you roll a double. You will not receive anything for any other outcome. How much should you be willing to pay for the privilege of rolling the dice?Level 1 A magazine subscription service is having a contest in which the prize is 80,000. If the company receives 1 million entries, what is the expectation of the contest?Level 1 A box contains one each of 1,5,10,20, and 100 bills. You reach in and withdraw one bill. What is the expected value?Level 1 A box contains one each of 1,5,10,20, and 100 bills. It costs 20 to reach in and withdraw one bill. What is the expected value?Level 1 Suppose that you have 5 quarters, 5 dimes, 10 nickels, and 5 pennies in your pocket. You reach in and choose a coin at random so that you can give it to your child. What is the expectation? What is the most likely gift?Level 1 A game involves tossing two coins and receiving 50 if they are both heads. What is a fair price to pay for the privilege of playing?Level 1 Krinkles potato chips is having a Lucky Seven Sweepstakes. The one grand prize is 70,000;7 second prizes each pay 7,000; 77 third prizes each pay 700; and 777 fourth prizes each pay 70. What is the expectation of this contest, if there are 10 million entries?Level 1 A punch-out card contains 100 spaces. One space pays 100, five spaces pay 10, and the others pay nothing. How much should you pay to punch out one space?Level 2 What is the expectation for the 1 bets in Problems 2130 on a U.S. roulette wheel? See Figure 13.8 on page 616. Black22PS23PS24PSLevel 2 What is the expectation for the 1 bets in Problems 2130 on a U.S. roulette wheel? See Figure 13.8 on page 616. Three-number bet26PS27PSLevel 2 What is the expectation for the 1 bets in Problems 2130 on a U.S. roulette wheel? See Figure 13.8 on page 616. Six-number bet29PS30PSLevel 2 Consider the spinners in Problems 31-34. Determine which represent fair games. Assume that the cost to spin the wheel once is 5.00 and that you will receive the amount shown on the spinner after its stops.32PSLevel 2 Consider the spinners in Problems 31-34. Determine which represent fair games. Assume that the cost to spin the wheel once is 5.00 and that you will receive the amount shown on the spinner after its stops.Level 2 Consider the spinners in Problems 31-34. Determine which represent fair games. Assume that the cost to spin the wheel once is 5.00 and that you will receive the amount shown on the spinner after its stops.Level 2 Assume that a dart is randomly thrown at the dartboard shown here and strikes the board every time. The payoffs are listed on the board. How much should you be willing to pay for the opportunity to play this game? 1.00 6.00 8.00 10.00 4.00Level 2 Assume that a dart is randomly thrown at the dartboard shown here and strikes the board every time. The payoffs are listed on the board. How much should you be willing to pay for the opportunity to play this game? 16 5 8 2 1 4Level 2 In old gangster movies on TV, you often hear of number runners or the number racket. This numbers game, which is still played today, involves betting 1 on the last three digits of the number of stocks sold on a particular day in the future as reported in The wall street Journal. If the payoff is 500, what is the expectation for this numbers game?38PS39PSLevel 2 A realtor who takes the listing on a house to be sold knows that she will spend 800 trying to sell the house. If she sells it herself, she will earn 6 of the selling price. If another realtor sells a house from her list, the first realtor will earn only 3 of the price. If the house remains unsold after 6 months, she will lose the listing. Suppose that the probabilities are follows: Event Probability Sells the house alone 0.50 Sells through another agent 0.30 Does not sell in 6 months 0.20 What is the expected profit from listing a 185,000 house?Level 2 An oil-drilling company knows that it costs 25,000 to sink a test well. If oil is hit, the income for the drilling company will be 425,000. If only natural gas is hit, the income will be 125,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and if the probability of hitting gas is 1/20, what is the expectation for the drilling company? Should the company sink the test well?Level 2 In Problem 41, suppose that the income for hitting oil is changed to 825,000 and the income for the gas to 225,000. Now what is the expectation for the drilling company? Should the company sink the test well?Level 2 Consider the following game in which a player rolls a single die. If a prime 2, 3, or 5 is rolled, the player wins 2. If a square 1 or 4 is rolled, the player wins 1. However, if the player rolls a perfect number 6, it costs the player 11. Is this a good deal for the player or not?Level 2 A game involves drawing a single card from an ordinary deck. If an ace is drawn, you receive 50; if a face card is drawn, you receive 25; if the two of spades is drawn, you receive 1. If the cost of playing is 10, should you play?Level 2 A company held a contest, and the following information was included in the fine print: Prize Number of Prizes Probability of Winning 10,000 13 0.000005 1,000 52 0.00002 100 520 0.0002 10 28,900 0.010886 TOTAL 29,485 0.011111 Read this information carefully, and calculate the expectation to the nearest cent for this contest.Level 2 A company held a bingo contest for which the following chances of winning were given: Playing One Card, Your Chances Of Winning Are at Least: 1 Time 7 Times 13 Times 25 1 in 21,252 1 in 3,306 1 in 1,635 3 1 in 2,125 1 in 304 1 in 163 1 1 in 886 1 in 127 1 in 68 Any prize 1 in 609 1 in 87 1 in 47 What is the expectation to the nearest cent from playing one card 13 times?Level 2 Heights in inches obtained by a group of people in a random survey are reported in the following table: Height Probability 55 0.001 60 0.022 65 0.136 70 0.341 75 0.341 80 0.136 85 0.022 90 0.001 What is the expected height in inches?Level 2 In a certain school, the probabilities of the number of students who are reported tardy are shown in the following table: Number tardy: 0 1 2 3 4 Probability: 0.15 0.25 0.31 0.21 0.08 What is the expected number of tardies rounded to two decimal places?Level 2 Calculate the expectation to the nearest cent for the Readers Digest sweepstakes described. Assume there are 197,000,000 entries.50PS51PS52PS53PS54PS55PS56PSProblem Solving Level 3 HISTORICAL QUEST The Swiss mathematician Daniel Bernoulli 1700-1782 was part of the famous Bernoulli family see Historical Note in Section 8.3. In 1738 he published the book St. Petersburg Academy Proceedings in which the problem known as the St. Petersburg Paradox was first published. To understand this paradox, you must first work Problems 5760 together. The paradox is seen after you answer the question in Problem 60. Suppose you toss a coin and will win 1 if it comes up heads. If it comes up tails, you toss again. This time you will receive 2 if it comes up heads. If it comes up tails, toss again. This time you will receive 4 if it is heads and nothing if it comes up tails. What is the mathematical expectation for this game?Problem Solving Level 3 HISTORICAL QUEST The Swiss mathematician Daniel Bernoulli 1700-1782 was part of the famous Bernoulli family see Historical Note in Section 8.3. In 1738 he published the book St. Petersburg Academy Proceedings in which the problem known as the St. Petersburg Paradox was first published. To understand this paradox, you must first work Problems 5760 together. The paradox is seen after you answer the question in Problem 60. Suppose you toss a coin and will win 1 if it comes up heads. If it comes up tails, you toss again. This time you will receive 2 if it comes up heads. If it comes up tails, toss again. This time you will receive 4 if it is heads. Continue in his fashion for a total of 10 flips of the coin, after which you receive nothing if it comes up tails. What is the mathematical expectation for this game?59PS60PSIN YOUR OWN WORDS What is the fundamental counting principle?2PS3PS4PS5PS6PSWhich of the following is more probable? A. Flipping a coin 3 times and obtaining at least 2 heads B. Flipping a coin 4 times and obtaining at least 2 heads8PSWhich of the following is more probable? A. Correctly guessing all the answers on a 20-question true-false examination B. Flipping a coin 20 times and obtaining all heads10PSFind the requested probabilities in Problems 11-14. PA- if PA=0.612PSPC ifPC-=91314PS15PSChoose a natural number between 1 and 100, inclusive. What is the probability that the number chosen is not a multiple of 5?Three fair coins are tossed. What is the probability that at least one is a head?Find the probability of obtaining at least one head in four flips of a coin.What are the odds in favor of drawing an ace from an ordinary deck of cards?What are a four-child familys odds against having four boys?The probability of drawing a heart from a deck of cards is 14; what are the odds against drawing a heart?Suppose the probability of an event is 0.80. What are the odds in favor of this event?23PSRacetracks quote the approximate odds for each race on a large display board called a tote board. Heres what it might say for a particular race: Horse Number Odds 1 18 to 1 2 3 to 2 3 2 to 1 4 7 to 5 5 1 to 1 What will be the probability of winning for each of these horses? Note: The odds stated are for the horses losing. Thus, Phorse1losing=1818+1=1819 So Phorse1winning=1-1819=11925PSSuppose the odds are 33 to 1 that someone will lie to you at least once in the next seven days. State this as a probability.27. Suppose that a family want to have four children. a. What is the sample space? b. What is the probability of 4 girls? 4 boys? c. What is the probability of 1 girl and 3 boys? 1 boy and 3 girls? d. What is the probability of 2 boys and 2 girls? e. What is the sum of your answers in parts b through d?28PS29PS30PSA single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen or king. PfacecardjackA single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen or king. PjackfacecardA single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen or king. Pheartnotaspade34PS35PSA single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen or king. PjackblackTwo cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in Problems 37-42. PacetwoTwo cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in Problems 37-42. PkingkingTwo cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in Problems 37-42. Pheartheart40PSTwo cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in Problems 37-42. PblackredTwo cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in Problems 37-42. PblackblackWhat is the probability of getting a license plate that has a repeated letter or digit, if you live in a state in which license plates have two letters followed by four numerals?What is the probability of getting a license plate that has a repeated letter or digit, if you live in a state in which license plates one numeral followed by three letters followed by three numerals?45. Consider the following table showing the results of a survey of TV network ececutives. Opinion of Current Programming Network Satisfied, S Not Satisfied, S Total NBC, N 18 7 25 CBS, C 21 9 30 ABC, A 15 10 25 Total 54 26 80 Suppose one network executive is selected at random. Find the indicated probabilities. a. What is the probability that it is an NBC executive? b. What is the probability that the selected person is satisfied? c. What is the probability the selected person is from CBS if we know the person is satisfied with current programming? d. What is the probability the selected person is satisfied if we know the person is from CBS?46. Suppose a single die is rolled. Find the probabilities. a. 6, given that an odd number was rolled. b. 5, given that an odd number was rolled. c. odd, given that the rolled number was a 6 d. odd, given that the rolled number was a 547PS48PS49. Suppose a pair of dice is rolled. Consider the sum of the numbers on the top of the dice and find the probabilities. a. 7, given that the sum is odd b. odd, given that a 7 was rolled c. 7, given that at least one die came up 250. Suppose a pair of dice is rolled. Consider the sum of the numbers on the top of the dice and find the probabilities. a. 5, given that exactly one die came up 2 b. 3, given that exactly one die came up 2 c. 2, given that exactly one die came up 251PSShow that the odds against an event E can be found by computing PE/PE.53PSA sorority has 35 members, 25 of whom are full members and 10 of whom are pledges. Two persons are selected at random from the membership list of the sorority. Find the requested probabilities. a. The first person selected is a pledge. b. The first person selected is not a pledge. c. The second person selected is a pledge if the first person selected was also a pledge. d. The second person selected was a full member if the first person selected was a pledge. e. The second person selected is a pledge if the first person selected was a full member. f. The second person selected is a full member if the first person selected was also a full member. g. The second person selected was a pledge. h. Use a tree diagram to represent the indicated probabilities.IN YOUR OWN WORDS The odds against winning a certain lottery are a million to one. Make up an example to help visualize these odds.57PS58PS60PSIN YOUR OWN WORDS What do we mean by independent events?What is the formula for the probability of an intersection?3PS4PS5PS6PS7PS8PS9PS10PS