A bag contain `n` ball out of which some balls are white. If probability that a bag contains exactly `i` white ball is pro0portional to `i^2dot` A ball is drawn at random from the bag and found to be white, then find the probability that bag contains exactly 2 white balls.

Explanation

To solve the problem step by step, we will use Bayes' theorem and the information given about the probabilities of the number of white balls in the bag.

### Step 1: Define the Events
Let \( E_i \) be the event that there are exactly \( i \) white balls in the bag. The probability of this event is given to be proportional to \( i^2 \). Therefore, we can write:
\[ P(E_i) = \lambda i^2 \]
where \( \lambda \) is a constant of proportionality.
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