# card probability

• May 15th 2008, 05:36 PM
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?
• May 15th 2008, 06:17 PM
TheEmptySet
Quote:

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

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

To draw the next heart the is

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

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

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

I hope this helps (Worried)(Worried)
• May 15th 2008, 08:43 PM
Soroban
Hello, Beth!

Another approach . . .

Quote:

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: .$\displaystyle {52\choose2} = 1326$ possible outcomes.

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

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