Question

Ralph and Melissa watch lots of videos. But they have noticed that they don't agree very often. In fact, Ralph only likes about 10% of the movies that Melissa likes, i.e., P(Ralph likes a movie|Melissa likes the movie) = .10 They both like about 37% of the movies that they watch. (That is, Ralph likes 37% of the movies he watches, and Melissa likes 37% of the movies she watches.) If they randomly select a movie from a video store, what is the probability that they both will like it? prob. =

Answer 1

There is a 3.7% probability that they both will like it.

Explanation:

We can solve this problem using the Bayes rule derivation from conditional probability.

Bayes rule:

What is the probability of B, given that A?

`P(A/B) = (P(A \cap B))/(P(A))`

In this problem, we have that:

`P(A/B)` is the probability that Ralph likes the movie, given that Melissa likes. The problem states that this is 10%. So
`P(A/B) = 0.1`

`P(A)` is the probability that Melissa likes the movie. The problem states that
`P(A) = 0.37`.

If they randomly select a movie from a video store, what is the probability that they both will like it?

This is
`P(A \cap B)`.

`P(A/B) = (P(A \cap B))/(P(A))`

`P(A \cap B) = P(A)*P(A/B)`

`P(A \cap B) = 0.37*0.10 = 0.037`

There is a 3.7% probability that they both will like it.