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

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.

Step-by-step 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.