30% of all newly released films in theaters are animated movies. But just becaus

Question

30% 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, 11% of them are rated R. For all non-animated movies, 25% are rated R.

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) Here, we are given that:

P( animated ) = 0.3 and therefore P( non animated ) = 0.7

P( rated R | animated ) = 0.11
P( rated R | non animated ) = 0.25

Using law of total probability, we get:

P( rated R) = P( rated R | animated ) P( animated ) + P( rated R | non animated ) P( non animated )

P( rated R) = 0.11*0.3 + 0.25*0.7 = 0.208

Therefore 0.208 is the required probability here.

b) Probability that a random movie chosen is not rated R is computed as:

= 1 - P( rated R)

= 1 - 0.208

= 0.792

Therefore 0.792 is the required probability here.

c) Given that movie is not rated R, probability that the movie is not animated is computed as:

P( non animated | not rated R) = P( not rated R | non animated )P( non animated ) / P( not Rated R)

P( non animated | not rated R) = 0.75*0.7 / 0.792

P( non animated | not rated R) = 0.6629

Therefore 0.6629 is the required probability here.

d) Probability that the movie is either an animated movie or a movie not rated R is computed here as:

P( not rated R) + P( animated and rated R)

= P( not rated R) + P( rated R | animated )P(animated )

= 0.792 + 0.11*0.3

= 0.825

Therefore 0.825 is the required probability here.

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