A typical slot machine in a Nevada casino has three wheels, each marked with twe

Question

A typical slot machine in a Nevada casino has three wheels, each marked with twenty symbols equally spaced around the wheels. The machine is engineered so that on each play the three wheels spin independently, and each wheel is equally likely to show any one of its twenty symbols when it stops spinning. On the central wheel out of twenty symbols are stars, while there are two stars on the left wheel and three stars on the right wheel. The machine pays out the jackpot only if all three wheels come to rest showing a star. Calculate the probability of hitting the jackpot. Calculate the probability of getting exactly two stars.

Explanation / Answer

a) P(jackpot) = (2/20) x (10/20) x (3/20) = 0.0075

b) P(exactly two stars) = P(star on left and central wheel, but not on right) + P(star on left and right weel, but not on central) + P(star on central and right weel, but not on left)

= (2/20 x 10/20 x 17/20) + (2/20 x 10/20 x 3/20) + (18/20 x 10/20 x 3/20)

= 0.1175

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