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In: Statistics and Probability

Problem 1 Slot machines have three drums with the same number of positions on each drum....

Problem 1 Slot machines have three drums with the same number of positions on each drum. Each position contains a symbol. When you pull the lever on the machine, the drums spin. Assume that each drum is equally likely to stop in any position, and that the positions in which the three drums stop are independent of each other and independent from spin to spin. Suppose a particular slot machine has 9 positions on each drum, and that each position contains one of two symbols: an eggplant or a grapefruit. You win the jackpot if all three drums stop with eggplants showing. The first drum has 2 eggplants and 7 grapefruits, the second has 5 eggplants and 4 grapefruits, and the third drum has 4 eggplants and 5 grapefruits. A) In each pull of the lever, the probability of winning the jackpot is ____ B) The number of times I win the jackpot in 20 attempts has: a) an Hypergeometric distribution b) a negative binomial distribution d) a geometric distribution e) none of the above? C) The probability of winning the jackpot at least once in 20 attempts is ____ D) The number of attempts it takes to win the first jackpot has ____ E) The probability that it takes exactly 20 attempts to win the jackpot the first time is ____ F) The number of attempts it takes to win the jackpot for the sixth time has ____ G) The chance that I win the jackpot for the sixth time on my twentieth attempt is ____

Solutions

Expert Solution

The probability that the first drum stops with eggplants showing is

The probability that the second drum stops with eggplants showing is

The probability that the third drum stops with eggplants showing is ​​​​​​​

A) In each pull of the lever, the probability of winning the jackpot is  .

B) The number of times I win the jackpot in 20 attempts has Binomial distribution.

Correct choice is e) none of the above.

C)The probability of winning the jackpot at least once in 20 attempts is

D)The number of attempts it takes to win the first jackpot has Geometric distribution.

E) The probability that it takes exactly 20 attempts to win the jackpot the first time is  

F)The number of attempts it takes to win the jackpot for the sixth time has a negative binomial distribution.

G) Using negative binomial distribution, the required probability is

​​​​​​​

orchestra answered 2 years ago
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