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A and B are two events such that P(A) = 1/3, P(B) = 1/4, P(A + B) = 1/2, then P(B/A) is equal to:

a) 1/2
b) 1/3
c) 2/3
d) 1/4

User Fluffeh
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Final answer:

The conditional probability P(B|A) is calculated using the formula P(B|A) = P(A AND B) / P(A). Upon correcting the misinterpretation of P(A + B), we find P(B|A) = 1/4.

Step-by-step explanation:

The student has asked to find the conditional probability of event B given event A, represented as P(B/A). To find this, we need to use the formula for conditional probability: P(B|A) = P(A AND B) / P(A). We have P(A) = 1/3, P(A AND B) = P(A + B) - P(A) - P(B) since A and B are not mutually exclusive. Substituting the given values, we get P(A AND B) = 1/2 - 1/3 - 1/4. To solve this, we find a common denominator, which is 12, and get P(A AND B) = (6 - 4 - 3)/12 = -1/12. However, probabilities cannot be negative, indicating that there's been a misunderstanding in interpreting P(A + B) as the probability of both events occurring together, which isn't standard notation. Usually, P(A + B) means the probability of A or B occurring, not both. Assuming P(A + B) represents P(A OR B), we use P(A OR B) = P(A) + P(B) - P(A AND B). Rearranging gives us P(A AND B) = P(A) + P(B) - P(A OR B), which results in P(A AND B) = 1/3 + 1/4 - 1/2 = (4 + 3 - 6) / 12 = 1/12. Now we can find P(B|A) = P(A AND B) / P(A) = (1/12) / (1/3) = 1/4. Therefore, the answer is d) 1/4.

User SvenG
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