Question

a standard deck of 52 playing cards contains 13 cards in each of four suits: diamonds, hearts, clubs, and spades. two cards are chosen from the deck at random. what is the approximate probability of choosing one club and one heart? 0.0548 0.0637 0.1176 0.1275

Explanation:

Step1: Calculate number of ways to choose 1 club and 1 heart

The number of ways to choose 1 club out of 13 is $C(13,1)=\frac{13!}{1!(13 - 1)!}=13$. The number of ways to choose 1 heart out of 13 is $C(13,1)=\frac{13!}{1!(13 - 1)!}=13$. By the multiplication - principle, the number of ways to choose 1 club and 1 heart is $13\times13 = 169$.

Step2: Calculate total number of ways to choose 2 cards from 52

The number of ways to choose 2 cards from 52 is $C(52,2)=\frac{52!}{2!(52 - 2)!}=\frac{52\times51}{2\times1}=1326$.

Step3: Calculate the probability

The probability $P$ of choosing 1 club and 1 heart is $P=\frac{169}{1326}\approx0.1275$.

Answer:

0.1275