It is known that P(A) = 0.3, P(B) = 0.65, P(A and B) = 0.15 and P(A or B) = 0.8. Given that A occurs, what is the probability that B also occurs
Question
Given Data
- P(A) = 0.3
- P(B) = 0.65
- P(A and B) = 0.15
- P(A or B) = 0.8
Question
Given that A occurs, what is the probability that B also occurs?
Solution
The probability that B occurs given that A occurs is defined as the conditional probability P(B|A). This can be calculated using the formula:
P(B|A) = P(A and B) / P(A)
From the question, we know that P(A and B) = 0.15 and P(A) = 0.3. Substituting these values into the formula gives:
P(B|A) = 0.15 / 0.3 = 0.5
Therefore, given that A occurs, the probability that B also occurs is 0.5.
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