Question

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: 75% of the females attended the romantic comedy. Among the male moviegoers the romantic comedy also was more popular: 60% 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, (If necessary, consult a list of formulas.) P(XP) - —P(POR) = 0 P(F)- - P(POR)- O P(RIP) 0.25 P(R ) - 0.6 P( FR)= 0 P(F) 07 P( FR) - O (17) - 0 What is the probability that a randomly chosen moviegoer attended the warm Continue

Answer 1

PCR/F) 0.5 11 P(FnR) O.22 PCF)-0.3 PCFOR) PCB/F) =0.25 PCR/E0 P(FlOR) P(F'nR) O.42 P (F)= =0. O.28 1-1 PCRIF0.4 PE P(R/E)P(F) PCB/ P(was Phinm) 1 O.28 O.070 O.355 1