# Thread: card probability

1. ## card probability

Need help with this problem in a hurry

If 2 cards are drawn from a deck of 52 cards and not replaced, what is the probability that both cards will be hearts?

2. Originally Posted by Beth shaske
Need help with this problem in a hurry

If 2 cards are drawn from a deck of 52 cards and not replaced, what is the probability that both cards will be hearts?
If I remember correctly the is a reduced samplespace problem.

the prob of drawing the first heart is

$\frac{13}{52}=\frac{1}{4}$

To draw the next heart the is

$\frac{12}{51}=\frac{4}{17}$

This is because of the 51 cards left 11 are hearts.

The the probability is $\frac{1}{4} \cdot \frac{4}{17}=\frac{1}{17}$

I hope this helps

3. Hello, Beth!

Another approach . . .

If 2 cards are drawn from a deck of 52 cards and not replaced,
what is the probability that both cards will be Hearts?
There are: . ${52\choose2} = 1326$ possible outcomes.

There are: . ${13\choose2} = 78$ ways to draw two Hearts.

Therefore: . $P(\text{2 Hearts}) \;=\;\frac{78}{1326} \;=\;\boxed{\frac{1}{17}}$