Question

A school has two varsity basketball teams. One is the girls' team, and the other is the boys' team. On any given Saturday in December, the probability that the girls' team will have a game is 0.8, and the probability that the boys' team will have a game is 0.7. The probability that both teams have games is 0.65.
On any given Saturday in December, what is the probability that either the girls' team or the boys' team has a game?
Answer choices:
0.65
0.7
0.8
0.85

Answer 1

The probability that either the girls' or boys' team gets a game is 0.85            

Step-by-step explanation:

Step 1:

Let P(G) represent the probability of girls team getting a game and P(B) represent the probability of the boys team getting a game.

P(B ∪ G) represents the probability of either girls and boys team getting a game.

P(B ∩ G) represents the probability of both girls and boys team getting a game.

Step 2:

It is given that P(G) = 0.8, P(B) = 0.7 and P(B ∩ G) = 0.65

We need to find the probability of either girls or boys team getting a game which is represented by P(B ∪ G)

Step 3:

P(B ∪ G) = P(B) + P(G) - P(B ∩ G)

= 0.8 + 0.7 - 0.65 = 0.85

Step 4:

Answer:

The probability that either the girls' or boys' team gets a game is 0.85