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P(F n R) = P(R|F) - P(R|F) - 0.65 P(F n R) - 0 P(F F = 0.7 r(Fn F) - P P(R|F) - What is the probability that a randomly chosen moviegoer attended the romantic comedy?

P(F n R) = P(R|F) - P(R|F) - 0.65 P(F n R) - 0 P(F F = 0.7 r(Fn F) - P P(R|F) - What is the probability that a randomly chosen moviegoer attended the romantic comedy?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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For a recent evening at a small, old-fashioned movie theater, 30% of the moviegoers were female and 70% were male. There were two movies playing that evening. One was a romantic comedy, and the other was a World War II film. As might be expected, among the females the romantic comedy was more popular than the war film: 85% of the females attended the romantic comedy. Among the male moviegoers the romantic comedy also was more popular: 65% of the males attended the romantic comedy. No moviegoer attended both movies. Let F denote the event that a randomly chosen moviegoer (at the small theater that evening) was female and F denote the event that a randomly chosen moviegoer was male. Let r denote the event that a randomly chosen moviegoer attended the romantic comedy and R denote the event that a randomly chosen moviegoer attended the war film. Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses.
Transcribed Image Text:For a recent evening at a small, old-fashioned movie theater, 30% of the moviegoers were female and 70% were male. There were two movies playing that evening. One was a romantic comedy, and the other was a World War II film. As might be expected, among the females the romantic comedy was more popular than the war film: 85% of the females attended the romantic comedy. Among the male moviegoers the romantic comedy also was more popular: 65% of the males attended the romantic comedy. No moviegoer attended both movies. Let F denote the event that a randomly chosen moviegoer (at the small theater that evening) was female and F denote the event that a randomly chosen moviegoer was male. Let r denote the event that a randomly chosen moviegoer attended the romantic comedy and R denote the event that a randomly chosen moviegoer attended the war film. Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses.
P (R |F) = 0.85 P(F) - O P(F n R) = P(F n F): P(E|F) - P(R|F) - 0.65 P(F n R) - 0 0.7 P(Fn F) = 0 P(R|F) - What is the probability that a randomly chosen moviegoer attended the romantic comedy?
Transcribed Image Text:P (R |F) = 0.85 P(F) - O P(F n R) = P(F n F): P(E|F) - P(R|F) - 0.65 P(F n R) - 0 0.7 P(Fn F) = 0 P(R|F) - What is the probability that a randomly chosen moviegoer attended the romantic comedy?
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