52. Two urns A and B contain 6 black and 4 white, 4 black and 6 white balls respectively.
Two balls are dawn from one of the urns. If both the ball drawn are white, find the
probabivity that the balls are drawn from urn B.
Answers
When both are white balls, probabivity that the balls are drawn from urn B = 5/7
Step-by-step explanation:
Given: Two urns A and B contain 6 black and 4 white, 4 black and 6 white balls respectively. Two balls are drawn from one of the urns.
To find: If both the ball drawn are white, find the probability that the balls are drawn from urn B.
Solution:
Let E1 = event of choosing urn A.
E2 = event of choosing urn B
Let E = event of drawing 2 white balls
P(E1) = P(E2) = 12
P(E/E1) = Probability that balls drawn are both white, given that balls are drawn from urn A = 4C2 / 10C2 = 6/45.
P(E/E2) = Probability that balls drawn are both white, given that balls are drawn from urn B = 6C2 / 10C2 = 15/45
P(E2/E) = [P(E2) × P(E/E2)] / [P(E1) × P(E/E1)] + [P(E2) × P(E/E2)]
= [ 1/2 * 15/45] / [(1/2 * 6/45) + (1/2 * 15/45)]
= (15/90) / (21/90)
= 15/21
= 5/7