Question

Urn A contains 7 white and 3 black balls; urn B contains 4 white and 6 black balls; urn C contains 2 white and 8 black balls. One of these urns is chosen at random with probabilities 0.2, 0.6 and 0.2 respectively. From the chosen urn, two balls are drawn at random without replacement. Both the balls happen to be white. Find the probability that the balls are drawn are from urn C.

Answer 1

Let A : Ball is drawn from bag A 

B : Ball is drawn from bag B 

C : Ball is drawn from bag C 

BB : Black ball 

WB : White ball 

RB : Red ball 

Probability of picking 2 white balls fro urn A = \(\frac{7c2}{10c2}\) = \(\frac{21}{45}\)

Probability of picking 2 white balls fro urn B = \(\frac{4c2}{10c2}\) = \(\frac{6}{45}\)

Probability of picking 2 white balls fro urn C = \(\frac{2c2}{10c2}\) = \(\frac{1}{45}\)

We want to find the probability of 2 white balls picked from urn C

Conclusion: Therefore, the probability of both selected white balls are from urn C is  \(\frac{1}{40}\)