If independent events A and B have P(A)=0.3 and P(B)=0.4, what is P(A and B)?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

If independent events A and B have P(A)=0.3 and P(B)=0.4, what is P(A and B)?

Explanation:
For independent events, the probability that both occur is the product of their probabilities. P(A and B) = P(A) × P(B) = 0.3 × 0.4 = 0.12. This value makes sense because the joint probability cannot exceed either individual probability, so it must be at most 0.3 and 0.4; 0.12 fits that constraint. The other numbers don’t fit the intersection: 0.7 is larger than both P(A) and P(B) and can't be the joint probability; 0.3 is just P(A) by itself, not the intersection; 0.52 is greater than 0.3, which is impossible for P(A and B).

For independent events, the probability that both occur is the product of their probabilities. P(A and B) = P(A) × P(B) = 0.3 × 0.4 = 0.12. This value makes sense because the joint probability cannot exceed either individual probability, so it must be at most 0.3 and 0.4; 0.12 fits that constraint.

The other numbers don’t fit the intersection: 0.7 is larger than both P(A) and P(B) and can't be the joint probability; 0.3 is just P(A) by itself, not the intersection; 0.52 is greater than 0.3, which is impossible for P(A and B).

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