Q. 85.0( 2 Votes )

# The bag A contains 8 white and 7 black balls while the bag B contains 5 white and 4 black balls. One balls is randomly picked up from the bag A and mixed up with the balls in bag B. Then a ball is randomly drawn out from it. Find the probability that ball drawn is white.

Answer :

Given:

Bag A contains 8 white and 7 black balls.

Bag B contains 5 white and 4 black balls.

A ball is transferred from bag A to bag B and then a ball is drawn from bag B.

There are two mutually exclusive ways to draw a white ball from bag B –

a. A white ball is transferred from bag A to bag B, and then, a white ball is drawn from bag B

b. A black ball is transferred from bag A to bag B, and then, a white ball is drawn from bag B

Let E_{1} be the event that white ball is drawn from bag A and E_{2} be the event that black ball is drawn from bag A.

Now, we have

We also have

Let E_{3} denote the event that white ball is drawn from bag B.

Hence, we have

We also have

Using the theorem of total probability, we get

P(E_{3}) = P(E_{1})P(E_{3}|E_{1}) + P(E_{2})P(E_{3}|E_{2})

Thus, the probability of the drawn ball being white is.

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