Answer to Question #87712 in Statistics and Probability for Julia

Question #87712
What is the probability of dealing two red cards from a standard deck of cards?
Round to the nearest thousands
1
Expert's answer
2019-04-08T13:21:34-0400

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=2652261521=25102=0.245.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


(262)=26!2!(262)!=325\binom{26}{2}={26! \over 2!(26-2)!}=325

Number of ways to choose 2 cards from 52 cards


(522)=52!2!(522)!=1326\binom{52}{2}={52! \over 2!(52-2)!}=1326

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


P=(262)/(522)=3251326=0.245P=\binom{26}{2}/\binom{52}{2}={325 \over 1326}=0.245


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