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

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

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)=(P(A\cap B))/(P(B))=(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)=(n(M\cap D))/(n(M))=(2)/(15)=0.133`

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