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., …

Question

asked May 8, 2020 234k views

1 Answer

BHP · Answer 1 · 2020-05-13T23:19:13+0000

Answer:

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.