A bag contains 4 balls. Two balls are drawn at random and are found to be white. What is the probability that all balls are white?

There are three possible cases. They are:

A₁: The bag has 2 white balls and 2 balls of other colour

A₂: The bag has 3 white balls and 1 ball of other colour

A₃: The bag has 4 white balls

Now, P (A₁) = P (A₂) = P (A₂) =

Let E be the event of selecting 2 white balls.

Applying Bayes Theorem:

Thus, the required probability is .

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