Question

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A)= 0.30 and P(B)= 0.40.

Assume that we have two events, A and Br that are mutually exclusive. Assume further that we know P(A) 0.30 and PCB 0.40 If an amount is zero, enter "0". a. What is P(An B)? b. what is p(AIB? C. Is AIB) equal to A)? Are events A and B dependent or independent? d. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement acurate? e. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

Answer 1

a. As A and B are mutually exclusive,

$P(A \cap B) = 0$

b. P(A | B) = $P(A \cap B) /P(B) = 0$

c. No, P(A | B) is not equal to P(A).

P(A | B) = 0, P(A) = 0.30

As P(A | B) is not equal to P(A) , they are not independent.

d. No, the 2 concepts are not exactly the same.

e. Mutually exclusive events are not independent if the probability of events are non-zero.