Question

you are dealt one card from a 52 - card deck. find the probability that you are dealt a diamond or a picture card. click the icon to view a description of a standard deck of playing cards. the probability is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine number of diamonds

There are 13 diamonds in a 52 - card deck. So $n(\text{diamonds})=13$.

Step2: Determine number of picture cards

There are 12 picture cards (4 Jacks, 4 Queens, 4 Kings) in a 52 - card deck. So $n(\text{picture cards}) = 12$.

Step3: Determine number of diamond - picture cards

There are 3 diamond - picture cards (Jack, Queen, King of diamonds). So $n(\text{diamonds and picture cards})=3$.

Step4: Use the addition rule of probability

The addition rule for two events $A$ and $B$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of getting a diamond and $B$ is the event of getting a picture card.
Since $P(A)=\frac{n(A)}{n(S)}$, $P(B)=\frac{n(B)}{n(S)}$ and $P(A\cap B)=\frac{n(A\cap B)}{n(S)}$ with $n(S) = 52$ (total number of cards).
$P(\text{diamond or picture card})=\frac{13}{52}+\frac{12}{52}-\frac{3}{52}=\frac{13 + 12-3}{52}=\frac{22}{52}=\frac{11}{26}$.

Answer:

$\frac{11}{26}$