a standard deck of 52 playing cards contains 13 cards in each of four suits: diamonds, hearts, clubs, and…

Explanation:

Step1: Calculate total number of ways to choose 2 cards

The number of ways to choose 2 cards from 52 cards is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 52$ and $r=2$. So $C(52,2)=\frac{52!}{2!(52 - 2)!}=\frac{52\times51}{2\times1}=1326$.

Step2: Calculate number of ways to choose one club and one heart

There are 13 clubs and 13 hearts. The number of ways to choose one club out of 13 and one heart out of 13 is $C(13,1)\times C(13,1)$. Since $C(13,1)=\frac{13!}{1!(13 - 1)!}=13$, the number of favorable cases is $13\times13 = 169$.

Step3: Calculate the probability

The probability $P$ is the number of favorable cases divided by the total number of cases. So $P=\frac{169}{1326}\approx0.1275$.

Answer:

0.1275