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

Question

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 12 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 10 eggplants and 2 grapefruits, the second has 5 eggplants and 7 grapefruits, and the third drum has 11 eggplants and 1 grapefruit.

In each pull of the lever, the probability of winning the jackpot is __________?

The number of times I win the jackpot in 20 attempts has what kind of distribution? Binomial, geometric, negative binomial or hypergeometric or none?

Explanation / Answer

As all three drums are 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. So these all are independent events

So P(wiining the jackpot) = P ( Drum 1 shows eggplants) * P(Drum 2 show eggplant) * P ( drum 3 shows eggplant)

= (10/12) * ( 5/12) * ( 11/12) = 275/864 = 0.3182

the number of times i win the jackpot in 20 attempts will have binomial distribution

where P(X) = n C r * pX * ( 1-p) (20- x)

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