50% of all newly released films in theaters are animated movies. But just becaus

Question

50% of all newly released films in theaters are animated movies. But just because a film is animated doesnt mean it's necessarily suitable for children. Of these animated movies, 26% of them are rated R. For all non-animated movies, 55% are rated R. (It may be helpful to use a probability tree to answer the questions below.) Use a probability tree to answer the following questions (Round all answers to four decimals) a. A new movie was just released in theaters. What's the probability that it's animated and rated R? b. Your 8 year old nephew wants to see a new movie at the theater with you and wants to choose it at random. What's the probability the randomly chosen movie you see is not rated R? c. The clerk at the ticket office chooses a movie for both of you and tells you it's not rated R. Given this information, what's the probability the movie is not animated? d. You're fine to see either an animated movie or a movie not rated R. What's the probability the chosen movie fits your preferences?

Explanation / Answer

a)P(animated and rated R)=P(animated)*P(rated R|animated)=0.50*0.26=0.1300

b)P(not rated R)=P(animated and not rated R)+P(not animatd and not rated R)=0.50*(1-0.26)+0.5*(1-0.55)

=0.5950

c)

P(not animated|not rated R)=P(not animatd and not rated R)/P(not rated R)=0.5*(1-0.55)/0.5950=0.3782

d)

P(animated or not ratd R)=1-P(not animated and rated R)=1-0.5*0.55=0.7250

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