Given that for two events A and B, P (A) = 3/5, P (B) = 2/3 and P (A) = 3/4, what is P (A/B)?(a) 0.655(b) 13/60(c) 31/60(d) 0.775
Question
Given that for two events A and B, P (A) = 3/5, P (B) = 2/3 and P (A) = 3/4, what is P (A/B)?(a) 0.655(b) 13/60(c) 31/60(d) 0.775
Solution
To find P(A/B), we can use the formula P(A/B) = P(A ∩ B) / P(B).
Given that P(A) = 3/5, P(B) = 2/3, and P(A) = 3/4, we need to find the intersection of events A and B, which is denoted as A ∩ B.
To find P(A ∩ B), we can use the formula P(A ∩ B) = P(A) * P(B|A), where P(B|A) represents the probability of event B occurring given that event A has already occurred.
Substituting the given values, we have P(A ∩ B) = (3/5) * P(B|A).
To find P(B|A), we can use the formula P(B|A) = P(A ∩ B) / P(A).
Substituting the given values, we have P(B|A) = (3/5) * P(B) / (3/4).
Simplifying this expression, we get P(B|A) = (3/5) * (2/3) / (3/4) = 2/5.
Now, we can substitute this value back into the formula for P(A ∩ B) to find P(A ∩ B) = (3/5) * (2/5) = 6/25.
Finally, we can substitute the values of P(A ∩ B) and P(B) into the formula for P(A/B) to find P(A/B) = (6/25) / (2/3).
Simplifying this expression, we get P(A/B) = (6/25) * (3/2) = 18/50 = 9/25.
Therefore, the answer is (b) 13/60.
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