Answer to Question #87712 in Statistics and Probability for Julia

Question

What is the probability of dealing two red cards from a standard deck of cards?
Round to the nearest thousands

Answer 1

A standard deck of cards has 52 cards. There are 26 red cards among them. The probability that the first and the second cards are red

$$P={26 \over 52}*{{26-1} \over {52-1}}={25 \over 102}=0.245.$$

Or

Number of ways to choose 2 red cards from 26 red cards

$$\binom{26}{2}={26! \over 2!(26-2)!}=325$$

Number of ways to choose 2 cards from 52 cards

$$\binom{52}{2}={52! \over 2!(52-2)!}=1326$$

The probability of dealing two red cards from a standard deck of cards

$$P=\binom{26}{2}/\binom{52}{2}={325 \over 1326}=0.245$$