Question

Let A and B be two independent events
defined on sample space S. Which of the
following is true ?
А
P(either A occurs or B occurs) = P(A) +
P(B) - P(A)P(B)
B
P(either A occurs or B occurs) = 1 -
P(A)P(B)
C
P(either A occurs or B occurs) < P(AUB)​

Answer 1

Step-by-step explanation:

C). P(either A occurs or B occurs) < P(AUB)

Hope its help..

Answer 2

Answer: The answer is none of these (option D)

Step-by-step explanation:

A and B be two independent events defined on sample space S.

Now,

P(either A occurs or B occurs) = P(A occurs) + P (B occurs) - P(both A and B occurs)

=> P(either A occurs or B occurs) = P(either A occurs or B occurs) = P(A) + P(B) - P(A ∩ B)

Since A and B are independent events then P(A ∩ B) = 0

Therfore,

P(either A occurs or B occurs) = P(A) + P(B)

Now, P(AUB)​ = P(A) + P(B)  = P(either A occurs or B occurs) .

Therefore, options A, B, and C are not true.