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  • If A and B are mutually exclusive events, then A. P (A) ≤ P (B) B. P (A) ≥ P (B) C. P (A) < P (B​​​​​​​) D. none of these

If A and B are mutually exclusive events, then
A. P (A) ≤ P (\bar{B})

B. P (A) ≥ P (\bar{B})
C. P (A) < P (\bar{B})
D. none of these

Answers (1)

A & B are mutually exclusive events       …… (given)

Thus, P (A ∩ B) = 0

Now, P (A U B) = P (A) + P (B) – P (A ∩ B)        ……. (by general addition rule)

Thus, P (A U B) = P (A) + P (B) - P (A ∩ B)

P (A U B) = P (A) + P (B) – 0

P (A U B) = P (A) + P (B)

Now, for all events A, B

0 ≤P(A)≤1

Thus, P (A) + P (B) ≤ 1

P (A) ≤ 1 – P (B)

Thus, by complement rule,

P (A) ≤ P (\bar{B})

Thus, option A is the correct answer.

Posted by

infoexpert22

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