Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?

Step-by-step solution

From the given information E ₁= One white ball transferred from A to B then urn A contains White =1 , Black =2 and urn B contains White =4 , Black =2 E ₂= One Black ball transferred from A to B then urn A contains White =2 , Black =1 and urn B contains White =3 , Black =3 F = One white ball is drawn from urn B . aligned & P ( ~F )= P ( E ₁ ) P ( ~F / E ₁ )+ P ( E ₂ ) P ( ~F / E ₂ ) & = 2 4 4 6 + 2 4 3 6 = 8 24 + 6 24 = 14 24 = 7 12 aligned