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P(a ∩ b) = 0.2 and p(b) = 0.5, find p(a|b).

User Lavern
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Final answer:

To find the conditional probability P(A|B), we use the formula P(A|B) = P(A ∩ B) / P(B). With P(A ∩ B) = 0.2 and P(B) = 0.5, the calculation gives us P(A|B) = 0.4.

Step-by-step explanation:

The question is related to the concept of conditional probability in mathematics. Conditional probability, denoted as P(A|B), is the probability of event A occurring, given that event B has already occurred. The question provides that the probability of both events A and B occurring, P(A ∩ B), is 0.2 and the probability of event B occurring, P(B), is 0.5. To find the conditional probability of A given B, P(A|B), we will use the formula P(A|B) = P(A ∩ B) / P(B).

Given that P(A ∩ B) = 0.2 and P(B) = 0.5, we can calculate:

P(A|B) = P(A ∩ B) / P(B) = 0.2 / 0.5 = 0.4.

Therefore, the conditional probability of event A occurring given that event B has occurred is 0.4.

User Chau Giang
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