Bag A contains 3 white and 5 black balls while bag B contains 4 white and 3 black balls. A ball is selected at random from bag A and put in bag B. If a ball is now selected at random from bag B then the probability that this ball is white ball is...

Step-by-step solution

Let E₁ be the event that a white ball is transferred from bag A to bag B. Let E₂ be the event that a black ball is transferred from bag A to bag B. Let W be the event that a white ball is drawn from bag B. The probability of transferring a white ball from bag A is: P(E₁) = 3 8 The probability of transferring a black ball from bag A is: P(E₂) = 5 8 If E₁ occurs, bag B will contain 5 white and 3 black balls. The probability of drawing a white ball is: P(W|E₁) = 5 8 If E₂ occurs, bag B will contain 4 white and 4 black