The problem is as follows:

A person draws 3 balls from a bag containing 3 white, 4 red and 5 black balls. He is offered ₹10, ₹5 and ₹2 if he draws 3 balls of the same colour, 2 balls of the same colour and 1 ball of the same colour. Find his expectation.

My approach is:

Total expectation= P(3 balls are of the same colour)*10+ P(2 balls of the same colour)*5+ P(1 ball of each colour)*2.

Now, P(3 balls of same colour)= P(3 White coloured balls) + P(3 Red coloured balls) + P(3 Black coloured balls).

Similarly, calculate P(2 balls of same colour) and P(1 ball of each colour).

Am I right? If possible, please provide a detailed solution. Thanks.

The problem is as follows:

A person draws 3 balls from a bag containing 3 white, 4 red and 5 black balls. He is offered ₹10, ₹5 and ₹2 if he draws 3 balls of the samee colour, 2 balls of the same colour and 1 ball of each colour. Find his expectation.

My approach is:

Total expectation= P(3 balls are of the same colour)*10+ P(2 balls of the same colour)*5+ P(1 ball of each colour)*2.

Now, P(3 balls of same colour)= P(3 White coloured balls) + P(3 Red coloured balls) + P(3 Black coloured balls).

Similarly, calculate P(2 balls of same colour) and P(1 ball of each colour).

Am I right? If possible, please provide a detailed solution. Thanks.