If A and B are independent and P(A) = 0.4, what is P(A|B)?

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Study for the Descriptive Statistics and Introduction to Probability Test. Test your knowledge with multiple choice questions, each with detailed hints and explanations. Ace your exam with confidence!

Multiple Choice

If A and B are independent and P(A) = 0.4, what is P(A|B)?

Explanation:
Independence means the occurrence of B does not change the likelihood of A. The conditional probability is P(A|B) = P(A∩B)/P(B). If A and B are independent, P(A∩B) = P(A)P(B). So P(A|B) = [P(A)P(B)]/P(B) = P(A). Since P(A) = 0.4, we get P(A|B) = 0.4. The other values would require some dependence between A and B or a special case, which isn’t the situation here.

Independence means the occurrence of B does not change the likelihood of A. The conditional probability is P(A|B) = P(A∩B)/P(B). If A and B are independent, P(A∩B) = P(A)P(B). So P(A|B) = [P(A)P(B)]/P(B) = P(A). Since P(A) = 0.4, we get P(A|B) = 0.4. The other values would require some dependence between A and B or a special case, which isn’t the situation here.

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