Gatto’s Mini Casino has three slot machines. Two of the machines are working correctly: you win 50% of the time. However, the third machine is broken: you win only 20% of the time. The machines look identical from the outside, so you cannot tell which one is broken. (a) Joannie picks one of the machines uniformly at random. What is the probability of winning if she plays the game once? If instead she plays the game twice (on the same machine), what is the probability she wins both games? (b) Suppose Joannie sits picks one of the machines uniformly and plays it twice. If she wins both times (lucky!), What is the probability that Joannie’s machine is the broken machine? (c) Now suppose that if you play the game and win, you get a payout of $10; otherwise you win nothing. Suppose that Joannie chooses one of the slot machines uniformly at random and then plays the game twice on that machine. What is Joannie’s expected payout
Question 1. Gatto’s Mini Casino has three slot machines. Two of the machines are working correctly: you win
50% of the time. However, the third machine is broken: you win only 20% of the time. The machines look identical
from the outside, so you cannot tell which one is broken.
(a) Joannie picks one of the machines uniformly at random. What is the probability of winning if she plays the game
once? If instead she plays the game twice (on the same machine), what is the probability she wins both games?
(b) Suppose Joannie sits picks one of the machines uniformly and plays it twice. If she wins both times (lucky!),
What is the probability that Joannie’s machine is the broken machine?
(c) Now suppose that if you play the game and win, you get a payout of $10; otherwise you win nothing. Suppose
that Joannie chooses one of the slot machines uniformly at random and then plays the game twice on that
machine. What is Joannie’s expected payout
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