(Slot machines) At a casino there are two kinds of slot machines, which look quite inden- tical from the outside. In machines of type A, the winning probability is 5%. In machines of type B, the winning probability is 7%. We also know that 70% of the machines are of type A, and 30% are of type B. (a) A gambler picks a slot machine at random, and plays once. What is the probability that he wins? (b) If the gambler wins, what is the probability that the machine is of type B?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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(Slot machines) At a casino there are two kinds of slot machines, which look quite inden-
tical from the outside. In machines of type A, the winning probability is 5%. In machines of
type B, the winning probability is 7%. We also know that 70% of the machines are of type A,
and 30% are of type B.
(a) A gambler picks a slot machine at random, and plays once. What is the probability that
he wins?
(b) If the gambler wins, what is the probability that the machine is of type B?
Transcribed Image Text:(Slot machines) At a casino there are two kinds of slot machines, which look quite inden- tical from the outside. In machines of type A, the winning probability is 5%. In machines of type B, the winning probability is 7%. We also know that 70% of the machines are of type A, and 30% are of type B. (a) A gambler picks a slot machine at random, and plays once. What is the probability that he wins? (b) If the gambler wins, what is the probability that the machine is of type B?
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