DISCRETE MATH (Pigeonhole Principle) 1. A drawer contains a dozen brown socks and a dozen black socks, all unmatched. A man takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two socks if the same color?

Q: A section of a test has four true-false questions. A completed test is selected at random and the…

A: To find out all the 16 outcomes:

Q: The access code for a garage door consists of three digits. Each digit can be any number from 0…

A: Given Information : The access code for a garage door consists of three digits. Each digit can be…

Q: Does the problem, 'Fifty people purchase raffle tickets. Three winning ticketsare selected at…

A: 50 people purchased a raffle ticket  and there are 3 winning tickets  we have to find different ways…

Q: 5. A bag of 10 apples contains 2 rotten apples and 8 good apples. A shopper selects a sample of…

A: (a)To calculate the possible number of samples.Given:

Q: A keyboard has 7 keys: letters A-G. Suppose that a melody is created by playing four random keys.…

A: the 7th key can not be E,F,G. Hence for the 7th key we are left with only 4 choices.

Q: 5 Justin is tossing a quarter to determine which team gets the ball at the beginning of a football…

A: There are 2 possible outcomes: Head and tail. Ram will get the ball is head appears.  We can get…

Q: (b) Consider the 48-ball lottery game described above. Recall that the order of the numbers chosen…

A:

Q: 9. A bowl contains 10 blue balls and 10 green balls. A girl selects balls at random without looking…

A:

Q: There is a game of chance in a carnival. The game consists of a box with 25 balls where 9 are red, 6…

A: Given problem Given that   There is a game of chance in a carnival. The game consists of a box…

Q: statistics and probability There are 4 Biomedical Engineering and 4 Electronics Engineering…

A:

Q: A box contains 6 blue balls and 4 red balls. Two balls are drawn from the box, one after the other,…

A: Given info:A box contains 6 blue balls and 4 red balls. Two balls are drawn from the box, one after…

Q: The access code for a gym locker consists of three digits. Each digit can be any number from 0…

A: All possible numbers that can be present in the access code are (0,1,2,3,4,5). So, the 3 digit…

Q: Decide whether the exercise involves permutations or​ combinations, and then solve the problem.   A…

A: Note: according to our guidelines we can answer only first three subparts Given  A bag contains 5…

Q: A certain game involves tossing 3 fair coins, and it pays 11¢ for 3 heads, 5¢ for 2 heads, and 1¢…

A: The probability distribution of 3 tossed coin: The probability distribution of Profit Profit (x)…

Q: you flip a fair coin ten times: a) What is the most common mix of heads and tails you might see? How…

A: When we toss a coin there are two possible results which wre heads or tails with probability 1/2.…

Q: 5 A bag of marbles had 15 blue marbles and the rest were green. For a game, 16 marbles were chosen…

A: To find out the number of blue marbles.

Q: Four hundred people buy raffle tickets. Three winning tickets will be drawn at random. (a) If first…

A: Given: People buy raffle tickets = 400

Q: One hundred people purchase lottery tickets Three winning tickets will be selected at random If for…

A: Three prizes have different prize money so these are three separate positions  The first prize can…

Q: Subject: Statistics and Probability How many seven-digit numbers can be formed if the last number…

A: The number of digits formed is given by:

Q: One student is selected at random from this group of 200 (a) the student is a male? (b) the…

A: Contingency Table   Baseball Basketball Football Soccer Total Male 28 13 58 7 106 Female 26…

Q: -The experiment is rolling five dice. Even E is {all five dice show different numbers}. a) What is…

A: Given that , the experiment is rolling five dice. Hence , the total number of all possible outcomes…

Q: A certain game involves tossing 3 fair coins, and it pays 23¢ for 3 heads, 10¢ for 2 heads, and 2¢…

A:

Q: Cole has a can of marbles. The table shows the number of marbles of each color in the can. Marbles…

A: Given: Number of white marbles = 5 Number of polka dot marbles = 8 Number of striped marbles = 4…

Q: The mathematics faculty at a college consists of 11 professors,12 associate professors, 9 assistant,…

A: The mathematics faculty at a college consists of: 11 professors 12 associate professors 9 assistant…

Q: A bag contains an equal number of blue, green, pink, and red balls. If a ball is chosen at random…

A: Given, Number of blue, green, pink, and red balls are equal in the bag.  Number of times a ball is…

Q: A city council consist of seven Democrats and six Republicants . If a committe of four people is…

A:

Q: Bruce is playing a game. This is a game in which seven distinct random numbers are chosen from the…

A: Given, Bruce is playing a game in which seven distinct random numbers are chosen from the digits 1,…

Q: What is the theoretical probability of getting a 2 or a 3 when rolling a number cube?

A:

Q: Jerahmeel has some marbles in two bags. In one bag she has 3 orange, 3 black and 3 yellow marbles.…

A:

Q: The access code for a safe consists of three digits. Each digit can be any number from 1 through 9,…

A: For the given data Find all the required

Q: 6. Consider the process of a student showing up for an exam in the wrong classroom and have…

A:

Q: 8 Maya lists all the possible outcomes of spinning the spinners below one time each. Pink Blue Green…

A: Given: There are 3 spinners. Spinner 1: Pink, Blue Spinner 2 : Green, Purple Spinner 3 : Pink, Blue,…

Q: 8 dice are tossed. How many times do you expect at most 3 dice to show a number less than 3?

A: Given: n = 8  possible outcomes of a die: 1 , 2 , 3 , 4 , 5 , 6 Total number of outcomes = 6 Number…

Q: 6. A multiple choice test has 4 possible answers for each question a. If you guess an answer for a…

A:

Q: Rolling a pair of dice, how many elements or outcomes are there if you observe a 5 at least once?

A: The number of occurrence of observation involve in the event divided by the total number of outcome…

Q: Bruce flipped a penny 5 times. It landedm heads 2 times and tails 3 times. Ifhe flips the coin a 6th…

A:

Q: There are 49 fair coins in a bag and one double headed one. You take one coin out of the bag at…

A:

Q: (a) When playing Yahtzee, you roll five regular 6-sided dice. How many different outcomes are…

A: a)  5 dices, each can have 6 possible outcomes..  One of the outcomes can be "2 3 1 6 6"  Hence,…

Q: A box contains 7 white balls, 9 black balls, and 2 red balls. a) 8 How many red balls must be added…

A: Given that white =7 Black = 9 Red = 2 Total =18

Q: Decide whether the exercise involves permutations or combinations, and then solve the problem. A bag…

A: Note: Hi there! Thank you for posting the question. As there are multiple sub parts, according to…

Q: Statistics and probability .. "Gobang" is a popular game in which two players set counters on a…

A:

Q: At the start of the month, a dealer purchases four batteries and your warehouse staff selects…

A: Given, At the start of December, the warehouse contains 10 batteries, 3 of which are not fully…

Q: You flip a coin six times and keep a record of the results. In how many ways could you obtain at…

A:

Q: 5. Mo has 140 songs on his mp3 player. a) How many different possibilities are there for the first…

A: Topic:- permutations and combinations

Q: Y Ou are piaying a game involving a fair 6-sided die and a fair coin. First the die is rolled. If…

A: a. The probability of the number on the die evenly divisible by 3 is: 26=13 The probability of the…

Q: Roll a pair of fair six-sided dice and let X be 1 if the dice land showing the same number of spots,…

A: Solution

Q: Using the pigeonhole principle A drawer contains a dozen brown socks and a dozen black socks, all…

A: Given problem Given that   A drawer contains a dozen brown socks and a dozen black socks ,all…

Q: A game is played with the following rules. Two ordinary number cubes, each with six sides labeled 1…

A: The all-possible outcomes for tossing a pair of dice is defined as follows:

Q: The access code for a safe consists of three digits. Each digit can be any number from 0 through 9,…

A: a. There are 3 digits in a code each can take values 0-9. Hence each of the place of these 3 places…

Q: Please answer this question

A: Given that, Flip a fair coin 6 times. No.of possible outcomes is 26 is 64.

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.