Question

A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. find the probability that a male chosen at random watches drama.

Answer 1

Answer:

The probability that a male chosen at random watches drama is 0.1333.

Step-by-step explanation:

The complete question is:

A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. Find the probability that a male chosen at random watches drama.

                 Male      Female     Total

Sports          8              3               11

Drama          2              6               8

Comedy       5              6               11

Total            15             15             30

Solution:

The conditional probability of an event A give that another event B has already occurred is:

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{n(A\cap B)}{n(B)}$

Denote the events as follows:

M = a male was selected

D = a person's favorite genre is drama

The number of males in the survey is, n (M) = 15.

The number of males in the survey who watches drama is, n (M ∩ D) = 2.

Compute the probability that a male chosen at random watches drama as follows:

$P(D|M)=\frac{n(M\cap D)}{n(M)}=\frac{2}{15}=0.133$

Thus, the probability that a male chosen at random watches drama is 0.1333.