Let A and B be two events, P(A) = 0.4, P(B) = 0.6, P(A∩B) = 0.2，Find:P(A|B)(Please keep four decimal places
Question
Let A and B be two events,
- P(A) = 0.4
- P(B) = 0.6
- P(A ∩ B) = 0.2
Find: P(A|B) (Please keep four decimal places)
Solution
The conditional probability of event A given event B is denoted as P(A|B) and is calculated as:
P(A|B) = P(A ∩ B) / P(B)
where:
- P(A ∩ B) is the probability of both events A and B occurring
- P(B) is the probability of event B
In this case:
- P(A ∩ B) = 0.2
- P(B) = 0.6
Substituting these values into the formula, we get:
P(A|B) = 0.2 / 0.6 = 0.3333 when rounded to four decimal places.
So, the conditional probability of event A given event B is 0.3333.
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