Question

If you draw two cards from the deck at the same time, what is the probability that they will both be hearts?

Answer 1

The probability is 1/17.

Explanation:

The total number of ways in which 2 cards can be selected from a pack of 52 cards is
`\binom{52}{2}`

The total number of combinations of 2 cards with hearts equals
`\binom{13}{2}`

Thus the probability of the event that both the cards have hearts becomes

`P(E)=\frac{\binom{13}{2}}{\binom{52}{2}}=(1)/(17)`