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Denote by A, B, and C the events that a grand prize is behind doors A, B, and C, respectively. Suppose you randomly picked a door, say A. The game host opened a door, say B, and showed there was no prize behind it. Now the host offers you the option of either staying at the door that you picked (A) or switching to the remaining unopened door (C). Suppose the three doors have equal probability to have the grand prize. When you have picked a door, the host will then open one of the remaining doors that doesn't have the prize with equal probability. Use conditional probability to explain whether you should switch or not. (Hint: Denote by HB the event that the host opened door B. Let A, B and C represent the events that the prize is behind door A, door B, and door C, respectively. Focus on the events where you have opened door A and calculate P(H | A), P(H | B), and P(H | C).)

Denote by A, B, and C the events that a grand prize is behind doors A, B, and C, respectively. Suppose you randomly picked a door, say A. The game host opened a door, say B, and showed there was no prize behind it. Now the host offers you the option of either staying at the door that you picked (A) or switching to the remaining unopened door (C). Suppose the three doors have equal probability to have the grand prize. When you have picked a door, the host will then open one of the remaining doors that doesn't have the prize with equal probability. Use conditional probability to explain whether you should switch or not. (Hint: Denote by HB the event that the host opened door B. Let A, B and C represent the events that the prize is behind door A, door B, and door C, respectively. Focus on the events where you have opened door A and calculate P(H | A), P(H | B), and P(H | C).)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Denote by A, B, and C the events that a grand prize is behind doors A, B, and C, respectively. Suppose you randomly picked a door, say A. The game host opened a door, say B, and showed there was no prize behind it. Now the host offers you the option of either staying at the door that you picked (A) or switching to the remaining unopened door (C).
Transcribed Image Text:Denote by A, B, and C the events that a grand prize is behind doors A, B, and C, respectively. Suppose you randomly picked a door, say A. The game host opened a door, say B, and showed there was no prize behind it. Now the host offers you the option of either staying at the door that you picked (A) or switching to the remaining unopened door (C).
Suppose the three doors have equal probability to have the grand prize. When you have picked a door, the host will then open one of the remaining doors that doesn't have the prize with equal probability. Use conditional probability to explain whether you should switch or not. (Hint: Denote by HB the event that the host opened door B. Let A, B and C represent the events that the prize is behind door A, door B, and door C, respectively. Focus on the events where you have opened door A and calculate P(H | A), P(H | B), and P(H | C).)
Transcribed Image Text:Suppose the three doors have equal probability to have the grand prize. When you have picked a door, the host will then open one of the remaining doors that doesn't have the prize with equal probability. Use conditional probability to explain whether you should switch or not. (Hint: Denote by HB the event that the host opened door B. Let A, B and C represent the events that the prize is behind door A, door B, and door C, respectively. Focus on the events where you have opened door A and calculate P(H | A), P(H | B), and P(H | C).)
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