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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?

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?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Solve part a-c and explain how to get each answer
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? ! :0 F1 @ 2 F2 #3 80 F3 zoom $ 4 JAN 14 Q F4 % 5 g F5 MacBook Air ^ 6 F6 & 7 F7 * 00 8 DII F8 ( 9 F9 4 F10 Pro 04 an Set E I
Transcribed Image Text: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? ! :0 F1 @ 2 F2 #3 80 F3 zoom $ 4 JAN 14 Q F4 % 5 g F5 MacBook Air ^ 6 F6 & 7 F7 * 00 8 DII F8 ( 9 F9 4 F10 Pro 04 an Set E I
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