Answer:
P(B1|Black) = = 21/41 = 0.512
Step-by-step explanation:
In this question, we will use the <u>conditional probability</u> formula that is, for two events A and B, the probability that event A occurs given than event B has already occured is:
P(A|B) = P(A∩B)/P(B)
Here, we need to find the probability that the ball is from urn B1 given that it is black. i.e.
P(B1|Black) = P(B1∩Black) / P(Black)
P(B1∩Black) is the probability that the ball is chosen from B1 and it is black. The number of black balls in urn B1 is 3 and the total number of balls in this urn is 5. The probability of choosing either of the urns is 1/2.
So, P(B1∩Black) = (1/2) (3/5)
P(B1∩Black) = 3/10
P(Black) is the probability of selecting a black ball. this can be from either of the urns B1 and B2. So, we can calculate this probability as:
P(Black) = P(Black in B1) + P(Black in B2)
= (1/2)(3/5) + (1/2)(4/7)
P(Black) = 41/70
P(B1|Black) = P(B1∩Black) / P(Black)
= (3/10) / (41/70)
P(B1|Black) = 21/41 = 0.512
