Question

1. Show your work for the following

- If P(A) = 0.7, P(B) = 0.1 and A and B are mutually exclusive, find P (A or B).

- If P(A) = 0.5, P(B) = 0.4, and P(A or B) = 0.8, are A and B mutually exclusive?

- If P(B) = 0.6, find P(B^c).

2. Determine whether events A and B are mutually exclusive.

A: Jayden has a math class on Tuesdays at 2:00. B: Jayden has an English class on Tuesdays at 2:00.

3. In a statistics class of 30 students, there were 13 men and 17 women. Two of the men and three of

the women received an A in the course. A student is chosen at random from the class.

a. Find the probability that the student is a woman.

b. Find the probability that the student received an A.

c. Find the probability that the student is a woman or received an A.

d. Find the probability that the student did not receive an A.

Answer 1

1.a) If A and B are mutually exclusive, P(A or B) = P(A) + P(B)

= 0.7 + 0.1

= 0.8

b) P(A) + P(B) = 0.5 + 0.4 = 0.9

P(A or B) = 0.8

P(A or B) P(A) + P(B)

So, A and B are not mutually exclusive

c) P(B^c) = 1 - P(B)

= 1 - 0.6

= 0.4

2. Both events cannot occur at the same time. So, the events are mutually exclusive.

3. a) P(woman) = 17/30

b) P(received an A) = 5/30

= 1/6

c) P(woman or received an A) = (17 + 5 - 3)/30

= 19/30

d) P(student did not receive an A) = (30-5)/30

= 5/6