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?
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.FOM: Focus On Modeling: The Monte Carlo Method
Problem 3P: Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if...
Related questions
Question
Solve part a-c and explain how to get each answer
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Given information
VIEWStep 2: (a) Calculation of P (winning on a single play) and P (winning both times on the same machine)
VIEWStep 3: (b) Calculation of P (The broken machine was chosen given that Joannie won both times
VIEWStep 4: (c) Calculation of the Joannie's expected payout
VIEWSolution
VIEWStep by step
Solved in 5 steps with 33 images
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill