Question

you are dealt one card from a 52 - card deck. find the probability that you are dealt a club 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: Calculate number of clubs

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

Step2: Calculate 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: Calculate number of club - picture cards

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

Step4: Use the addition rule of probability

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here $A$ is the event of getting a club and $B$ is the event of getting a picture card.
$P(A)=\frac{n(A)}{n(S)}$, $P(B)=\frac{n(B)}{n(S)}$, $P(A\cap B)=\frac{n(A\cap B)}{n(S)}$, where $n(S) = 52$.
$P(\text{club or picture card})=\frac{13 + 12-3}{52}=\frac{22}{52}=\frac{11}{26}$.

Answer:

$\frac{11}{26}$