During a given month, P (A) = 0.75, P (B) = 0.6, and P (A and B) = 0.5. Are these two events independent? Are they mutually exclusive? A. yes; yes B. yes; no. no; yes C. no; no. D. it cannot be determined

Question

Gizmo

Mathematics

12 October, 21:40

During a given month, P (A) = 0.75, P (B) = 0.6, and P (A and B) = 0.5. Are these two events independent? Are they mutually exclusive? A. yes; yes B. yes; no. no; yes C. no; no. D. it cannot be determined

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Riley Clarke · Answer 1

Two events are mutually exclusive when the probability that both events happen equals the product of the probability that both events happen individually.

i. e. P (A and B) = P (A) x P (B)

Here, P (A and B) = 0.5 but P (A) x P (B) = 0.75 x 0.6 = 0.45

Therefore, the two events are not independent.

Two events are said to be mutually exclusive when P (A and B) = 0. Here P (A and B) ≠ 0.

Therefore, the two events are not mutually exclusive.

Therefore, option C is the correct answer.