A hand of three cards is drawn from an ordinary deck If it i

A hand of three cards is drawn from an ordinary deck. If it is known that two of the cards are the ace of spades and the ace of clubs, what is the probability that all three cards are aces?

Solution

3 cards are drawn from deck = 52 C 3

We know that First 2 cards drawn are ace of spade
and ace of club
And the Probaility of such selction is = 1 / 52 * 1/ 51

And drawing a Ace card from the remaning two Ace in pack = 2 C 1 / 50 C 1

Final probability = 1/52 * 1/51 * 2/50 = 0.0000150