Question

A certain town has two kinds of youth basketball teams. One is a school team (S) and the other is a rec team (R). On any given Saturday in December, the probability that a school team will have a game is 0.8, and the probability that a rec team will have a game is 0.7. The probability that both have games us 0.65.

On any given Saturday in December, what is the probability that either a rec team or a school team has a game?
Answer Choices:
0.65
0.7
0.8
0.85

Answer 1

D. 0.85

Explanation:

Given

Probability of S = 0.8

Probability of R = 0.7

Probability of S and R = 0.65

Required

Probability of S or R

Using probability notations;

P(S) = 0.8

P(R) = 0.7

P(S n R) = 0.65

The question requires that we solve for P(S or R)

For overlapping events S and R; the following formula is applicable.

P(S or R) = P(S) + P(R) - P(S n R)

Substitute the values of P(S), P(R) and P(S n R)

P(S or R) = 0.8 + 0.7 - 0.65

P(S or R) = 0.85

Hence, the probability that either a rec team or a school team has a game is 0.85