p(a)=1/3, p(b)=1/4.p(aub)=1/2. find p(a/b)?
To find the probability of A given B, denoted as P(A|B), we can use the formula:
P(A|B) = P(A∩B) / P(B)
We are given the following probabilities:
P(A) = 1/3
P(B) = 1/4
P(A∪B) = 1/2
First, let's find P(A∩B) using the formula:
P(A∩B) = P(A) + P(B) - P(A∪B)
P(A∩B) = 1/3 + 1/4 - 1/2
P(A∩B) = 4/12 + 3/12 - 6/12
P(A∩B) = 7/12 - 6/12
P(A∩B) = 1/12
Now, we can substitute the values into the formula for P(A|B):
P(A|B) = P(A∩B) / P(B)
P(A|B) = (1/12) / (1/4)
P(A|B) = (1/12) * (4/1)
P(A|B) = 4/12
P(A|B) = 1/3
Therefore, P(A|B) is equal to 1/3.