Answer :

Given:

The bag I contains 3 white and 2 black balls.

Bag II contains 2 white and 4 black balls.

A bag is chosen, and a ball is drawn from it.

There are two mutually exclusive ways to draw a white ball from one of the two bags –

a. The bag I is selected, and then, a white ball is drawn from the bag I

b. Bag II is selected, and then, a white ball is drawn from bag II

Let E_{1} be the event that bag I is selected and E_{2} be the event that bag II is selected.

Since there are only two bags and each bag has an equal probability of being selected, we have

Let E_{3} denote the event that a white ball is drawn.

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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