A gambling casino has two slot machines A and B. Any single use of a machine is

Question

A gambling casino has two slot machines A and B. Any single use of a machine is called an attempt. A person either wins or loses on any single attempt on either machine. The probability of winning at a single attempt on the machines is P(A) = p_a = 1/4 and P(B) = p_b = 1/3 respectively. Joe Zilch makes three separate, independent visits to the casino. On his first visit, he selects one machine at random and starts playing. Find his probability of winning on this first attempt. On his second visit, he selects one machine at random and starts playing. He wins once in three attempts on the machine he selected. Given these facts, find the probability that he initially chose machine A. On his third visit, he selects one machine at random and starts playing. He wins twice in four attempts on the machine he selected. Given these facts, find the probability of winning on his next attempt on this same machine.

Explanation / Answer

a.

1/4*1/3=1/12=0.08

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