Two cards are drawn at random from a pack of cards. The probability that both are the cards of the spade is

Question

Two cards are drawn at random from a pack of 52 cards. The probability that both are the cards of the spade is

Answer 1

Find the required probability:

In the question, it is given that two cards are drawn at random from a pack of 52 cards.

We know that there are 13 cards of spade.

So, the total number of ways of selecting two cards out of 13 cards is \({ }^{13} C_{2}\).

And the total number of ways of selecting two cards out of 52 cards is \({ }^{52} C_{2}\).

So, the required probability is given by \(\dfrac{{ }^{13} \mathrm{C}_{2}}{{ }^{52} \mathrm{C}_{2}}=\dfrac{13 \times 12}{52 \times 51}\).

Therefore, the required probability is \(\dfrac{1}{17}\).