Question

V. If P(A) 0.40, P(B)-0.80, and P(A and B) 0.35 a. Are A and B mutually exclusive? Explain why b. What is the probability of either A or B or both occurring? c. Using the multiplication rule, determine whether A and B are independent. d. What is the probability that neither A nor B will occur?

Answer 1

Ans 1. No, A and B are not mutually exclusive because P(A and B) is not equal to zero. For two events to be mutually exclusive P(A and B) should be equal to zero. A non-zero value indicates that the events can occur simultaneously.

Ans 2. P (A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.8 - 0.35 = 0.85.
Thus the probabilty of either A or B or both occuring is 0.85.

Ans 3. If A and B are independent events then P(A and B) = P(A)*P(B)
In this case, P(A)*P(B) = 0.4*0.8 = 0.32 and P(A and B) = 0.35

Hence, A and B are not independent events.

Ans 4. Probability of neither A nor B occuring = 1 - Probability of either A or B or both occuring
= 1 - 0.85
= 0.15