Melissa is looking for the perfect man. she claims that of the men at her college, 32% are smart. 33% are funny, and 16% are both smart and funny. use the venn diagram to answer the following question: if melissa is right, what is the probability that a man chosen at random from her college is neither funny nor smart? a. 0.51 b. 0.84 c. 0.67 d. none of the given answers is correct. e. 0.35

a. 0.51

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a men is smart.

B is the probability that a men is funny.

C is the probability that a mean is neither of those.

We have that:

In which a is the probability that a men is smart but not funny and is the probability that a men is both of these things.

By the same logic, we have that:

The sum of the probabilities is decimal 1, so:

.

We want to find C. We find the values of each of these probabilities, starting from the intersection.

16% are both smart and funny. This means that

33% are funny. This means that . So

.

32% are smart. This means that . So

.

Now we find C

.

The correct answer is:

a. 0.51