CGad knoNs and tells you that When the Nationals play Houston +hey areexpectedto Win ROOT0 df the time Close 8CTo Knows In a World Series aeter 3 pendent games what are the octls inde lead- Nationals will be ing the series 7 CHint Draw Probabilit Tree) 3 еvеrts 2n thein Nats win st aame dgesn't cnange adas game Game 3 own if the +he win and the Game Eame 1 W.2 x.2%2=.00% 2x.2x-3 W,2SX,2 032 4X.RX.8 W 4 .SX.X. 0.513 calco lations eont 329 O.1as घी 3.2To 03 2 (R.570 0. 12 2 0.1a8 312 (51.27o WAY di wnal did h test ale's d they addthesets Is this the ans? le 3.2%% 3. a 7o +3.270 0.u90 विनी ठ- what nappen aftu enn 12.६०)० 2.९०7० ALe $1.a90 89.70

CGad knoNs and tells you that When the Nationals play Houston +hey areexpectedto Win ROOT0 df the time Close 8CTo Knows In a World Series aeter 3 pendent games what are the octls inde lead- Nationals will be ing the series 7 CHint Draw Probabilit Tree) 3 еvеrts 2n thein Nats win st aame dgesn't cnange adas game Game 3 own if the +he win and the Game Eame 1 W.2 x.2%2=.00% 2x.2x-3 W,2SX,2 032 4X.RX.8 W 4 .SX.X. 0.513 calco lations eont 329 O.1as घी 3.2To 03 2 (R.570 0. 12 2 0.1a8 312 (51.27o WAY di wnal did h test ale's d they addthesets Is this the ans? le 3.2%% 3. a 7o +3.270 0.u90 विनी ठ- what nappen aftu enn 12.६०)० 2.९०7० ALe $1.a90 89.70

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.6: Counting Principles

Problem 74E: Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is...

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Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is played in 44 states, Washington D.C., Puerto Rico, and the U.S. Virgin Islands. The game is played by drawing five white balls out of a drum of 69 white balls (numbered 1-69) and one red powerball out of a drum of 26 red balls (numbered 1-26). The jackpot is won by matching all five white balls in any order and the red powerball. (a) Find the possible number of winning Powerball numbers. (b) Find the possible number of winning Powerball numbers when you win the jackpot by matching all five white balls in order and the red powerball.
There are 50 athletes signed up for a neighborhood basketball competition. Players can select to play in the 6-player games (“3 on 3”) or the 2-player games (“1 on 1”). All 50 athletes sign up for only one kind of game. Complete the table to show different combinations of games that could be played.
I offer you the following game. I have a bag that contains 3 red balls and 3 green balls. I will have you draw 2 without looking. If they are the same color, you win, if they are different colors, I win. Is the game fair? Support your answer with either a tree or the multiplication rule.
A person with $2 in her pocket bets $1, even money,on the flip of a coin, and she continues to bet $1 as longas she has any money. Draw a tree diagram to show thevarious things that can happen during the first four flipsof the coin. After the fourth flip of the coin, in how manyof the cases will she be(a) exactly even;(b) exactly $2 ahead?
In a TV show, there are three boxes. Red, Green, and Yellow. One of the boxes has afrog in it and the other 2 is empty. You are trying to avoid to open the box with the frog.Assume that you randomly selected a box, let’s say Green. The game host opens one ofthe unselected box, say Red, and showed there was no frog in it. The host knows whichone includes the frog. Now the host proposes you the option of either staying at the boxthat you have chosen or change it to the remaining box, (Yellow in this case). What is theprobability of finding the frog if you change your selection and if you don't change?Compare the results and make the decision about switching your initial selection. (I think the exact opposite monty hall problem)
In the Hackspace there are 3 Prusa 3D Printers, Hopper, Lovelace and Utting which have been running since the start of the year. • Hopper has done 30% of the total printing load. • Lovelace has done 22% of the total printing. • The rest of the printing was done on Utting. Hopper has had a 8% failure rate, Lovelace has had a 11% failure rate and Utting succeeds 96% of the time. (a) Draw a fully labelled tree diagram to show all the possible outcomes and their probabilities. (b) Find the probability that: i. A print will be done on Hopper and is successful ii. A print will fail iii. Given that a print has succeeded, what is the probability that it was printed on Lovelace
Powerball is a lottery game that is operated by the Multi-State Lottery Association and is played in 44 states, Washington D. C., Puerto Rico, and the U.S. Virgin Islands. The game is played by drawing five white balls out of a drum of 69 white balls (numbered 1-69) and one red powerball out of a drum of 26 red balls (numbered 1-26). The jackpot is won by matching all five white balls in any order and the red powerball. (a) Find the possible number of winning Powerball numbers. (b) Find the possible number of winning Powerball numbers when you win the jackpot by matching all five white balls in order and the red powerball.
Again consider a Little League team that has 15 playerson its roster.a. How many ways are there to select 9 players for thestarting lineup?b. How many ways are there to select 9 players for thestarting lineup and a batting order for the 9 starters?c. Suppose 5 of the 15 players are left-handed. Howmany ways are there to select 3 left-handed outfieldersand have all 6 other positions occupied by right-handedplayers?
In the board game Monopoly, if you end up in Jail, then on your turn you roll two fair 6-sideddice; if you roll doubles (the same number on both dice), you get out, and otherwise you stayin Jail and skip your turn. Usually you can also get out by paying a fine, but let’s say thatwe are playing with house rules that prevent that.Suppose that you’re playing Monopoly and it takes you more than six turns to get out ofJail. Given this information, what is the probability that it takes you exactly eight turns?
6. The varsity soccer team has 20 players. Three of the players are trained to be goalies while theremaining 17 can play any position. Only 11 of the players can be on the field at once.(a) We want to find the number of possible groups of 11 players the coach can choose. Is this apermutation or a combination?(b) If the coach wanted to choose her 11 starters at random by drawing names from a hat, how many possible groups of 11 starters could she choose?(c) The coach wants to make sure there is exactly one goalie on the field. How many ways can thecoach choose a lineup of 11 players if exactly 1 player must be a goalie?
A coin is tossed. If it shows heads, a marble is drawn from Box 1, which contains one white and one black marble. If it lands tails, a marble is drawn from Box 2, which contains two white and one black marble. Find: a) P(white| coin fell tails)
“ You are dealt five cards from a standard deck of 52 cards. How many of these handshave at least one queenandat least one spade. ”He breaks this into two cases. In the first case, he looks at hands which contain the queen of spadesQ♠. There is 1 way of choosing the Queen of Spades, and51C4ways of choosing the other fourcards. In the second case, he will start by choosing a non-spade queen (3 ways) and a non-queenspade (12 ways). There are 50 cards remaining, so he also throws away the Queen of Spades sothat he doesn’t overlap case 1. This gives49C3ways of choosing the last three cards. He concludesthat the answer is51C4+ (3·12·49C3). His answer is incorrect. Explain why, and give the correctanswer.