Question

3-12. If P(X A) 0.3, P(X B) 0.25, P(X C) 0.60, P(X A B) 0.55, and P(X B C) 0.70, determine the following probabilities. (a) P(X A) (b) P(X B) (c) P(X C) (d) Are A and B mutually exclusive

Answer 1

a) P(A')=0.7.

b) P(B')=0.75.

c) P(C')=0.4.

d) d) Therefore, we conclude that are A and B mutually exclusive events.

Explanation:

From task we know that are:

P(A)=0.3

P(B)=0.25

P(C)=0.6

Therefore, we get calculate the next probabilities:

a) P(A')=1-P(A)

P(A')=1-0.3

P(A')=0.7.

b) P(B')=1-P(B)

P(B')=1-0.25

P(B')=0.75.

c) P(C')=1-P(C)

P(C')=1-0.6

P(C')=0.4.

d) Therefore, we conclude that are A and B mutually exclusive events.