A slot machine has 3 wheels; each wheel has 20 symbols; the three wheels are independent...

A slot machine has 3 wheels; each wheel has 20 symbols; the three wheels are independent of each other. Suppose that the middle wheel has 11 cherries among its 20 symbols, and the left and right wheels have 2 cherries each.
a. You win the jackpot if all three wheels show cherries. What is the probability of winning the jackpot?

b. What is the probability that the wheels stop with exactly 2 cherries showing among them?

Solutions

Expert Solution

Solution :

A machine has 20 symbols.

the left and right wheels have 2 cherries each P(Left) = 2/20, P(Right) = 2/20

the middle wheel has 11 cherries among its 20 symbols P(Middle) = 11/20

probability of winning the jackpot if all three wheels show cherries =

P(Left and middle and Right) = P(Left) * P(Middle)* P(Right) = 2/20 * 11/20 * 2/20

probability of winning the jackpot if all three wheels show cherries = 0.0055

P(Left) = P(L) = 2/20 = 0.1,

P(Medium) = P(M) = 11/20 = 0.55,

P(Right) = P(R) = 2/20 = 0.1.

probability that the wheels stop with exactly 2 cherries showing among them is

probability that the wheels stop with exactly 2 cherries = 0.1035

orchestra answered 1 year ago

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