CA Foundation · Quantitative Aptitude · Probability
Two events A and B satisfy P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.25. Which statement is correct?
A and B are not independent. Independence needs the joint probability to equal the product of the individual probabilities, which is 0.5 × 0.4 = 0.20. The given joint probability is 0.25, so the test fails. They are not mutually exclusive either.
- AA and B are independent because P(A and B) is positive
- BA and B are mutually exclusive because P(A and B) is positive
- CA and B are independent because P(A and B) < P(A)
- DA and B are not independent because P(A)P(B) = 0.20 differs from 0.25Correct
Explanation
Independence requires P(A and B) = P(A)P(B). Here P(A)P(B) = 0.5 × 0.4 = 0.20, but P(A and B) = 0.25, so they are not independent. They are also not mutually exclusive, since the joint probability is not zero.
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