Refer to the Venn diagram below. What is the probability that a student plays football or baseball?

A
716

B
35

C
710

D
2833

See the Venn diagram corresponding to this question on the picture attached.

Explanation:

Call F the event playing football, P(F) the probability of playing football, S the event of playing baseball, P(S) the probability of playing baseball, K the event of playing basketball, and P(K) the probability of playing basketball.

The probability that a student plays football or baseball is P(F ∪ S)

By the properties of joint probabilities:

Each of the terms on the right-hand side of the equation can be calculated from the Venn diagram.

a) Number of total students represented on the Venn diagram:

b) Number of students that play football:

Therefore, P(F) = 40 / 66 = 20 / 33

c) Number of students that play baseball:

Therefore, P(S) = 24 / 66 = 4/11

d) Number of students that play both football and baseball:

Therefore, P (F ∩ S) = 8/66 =4/33

Finally:

28/33