Bayes Theorem(Probability)
Probability
Level
2
An urn B1 contains 2 white and 3 black balls and another urn B2 contains 3 white and 4 black balls. One urn is selected at random and a ball is drawn from it. If the ball drawn is found black, find the probability that the urn chosen was B1.
24/44
22/43
23/45
21/41
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1 solution
Step 1: Let E1, E2 denote the vents of selecting urns B1 and B2 respectively.
Then P(E1) = P(E2) = 12.
Let B denote the event that the ball chosen from the selected urn is black .
Then we have to find P(E1/B).
Step 2:
By hypothesis P(B/E1) = 35 and P(B/E2) = 47
By Bayes theorem P(E1/B) = P(E1)P(B/E1)/P(E1)P(B/E1)+P(E2)P(B/E2)
= 3/10/3*10+4/14
= 21/41