Answer:
There is a 3.7% probability that they both will like it.
Step-by-step 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?
In this problem, we have that:
is the probability that Ralph likes the movie, given that Melissa likes. The problem states that this is 10%. So
is the probability that Melissa likes the movie. The problem states that
.
If they randomly select a movie from a video store, what is the probability that they both will like it?
This is .
There is a 3.7% probability that they both will like it.