Question at position 11 If P(A) = 0.24 and P( B )=0.52 and A and B are independent, what is P(A or B)?0.12480.6352Approximately 00.760.28

Question

BlackTom AI · Accepted Answer

To evaluate P(A ∪ B) when A and B are independent, use the formula P(A ∪ B) = P(A) + P(B) − P(A)P(B).

Option 1: 0.1248
This value equals P(A) × P(B) (since 0.24 × 0.52 = 0.1248), not the probability of A or B happening together. It reflects the joint occurrence part, not the union, so it is not correct for P(A ∪ B).

Option 2: 0.6352
Compute P(A) + P(B) = 0.24 + 0.52 = 0.76. Then subtract P(A)P(B) = 0.24 × 0.52 = 0.1248. So 0.76 − 0.1248 = 0.6352. This matches the inclusion-exclusion formula for independent events, so this is the correct value for P(A ∪ B).

Option 3: Approximately 0
Saying the probability is approximately zero ignores the given probabilities 0.24 and 0.52 for A and B, and the fact that even after accounting for overlap via independence, the union probability is substantial (0.6352). Therefore this option is incorrect.

Option 4: 0.76
This is simply P(A) + P(B) without subtracting the overlap term P(A)P(B). Since A and B are independent, the overlap must be removed when forming the union, so 0.76 overstates P(A ∪ B). Hence this option is incorrect.

Option 5: 0.28
This value does not align with either P(A) + P(B) (which is 0.76) or P(A)P(B) (which is 0.1248). It misrepresents both individual probabilities and their interaction, so it is incorrect.

Question at position 11 If P(A) = 0.24 and P( B )=0.52 and A and B are independent, what is P(A or B)?0.12480.6352Approximately 00.760.28

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