34% of all newly released films in theaters are animated movies. But just becaus

Question

34% of all newly released films in theaters are animated movies. But just because a film is animated doesn’t mean it’s necessarily suitable for children. Of these animated movies, 13% of them are rated R. For all non-animated movies, 15% are rated R.

Round all answers to four decimal places.

Suggestion: Use a probability tree to answer the questions.

a. A new movie was just released in theaters. What is the probability that it’s animated and rated R?

b. Your eight year-old nephew wants to see a new movie at the theater with you and wants to choose it at random. What is 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 is the probability the movie is not animated?

d. You’re fine to see either an animated movie or a movie not rated R. What is the probability the chosen movie fits your preferences?

Explanation / Answer

a)probability that it’s animated and rated R =P(animated)*P(rated R|animated)=0.34*0.13=0.0442

b)

probability the randomly chosen movie you see is not rated R =P(animated and not rated R +non animated and not rated R)=0.34*(1-0.13)+(1-0.34)*(1-0.15)=0.8568

c)probability the movie is not animated given nit rated R =P(+non animated and not rated R)/P(not rated R)

=(1-0.34)*(1-0.15)/0.8568=0.6548

d)

probability =1-P(non animated and rated R) =1-(1-0.34)*0.15=0.901

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