Question

A single card is chosen at random from a standard deck of 52 playing cards. What is the probability that the card will be a club or a king?

• A. $\frac{1}{13}$
• B. $\frac{3}{13}$
• C. $\frac{1}{4}$
• D. $\frac{4}{13}$

Answer 1

The correct option is D $\frac{4}{13}$

Let E be the event that chosen card is club and F be the event that chosen card is king
.Number of elements in E is 13.
Number of elements in F is 4.
$\therefore P\left(E\right)=\frac{13}{52}$ and
$P\left(F\right)=\frac{4}{52}$
There is only one card in club which is king also,
i.e., $n(E\cap F)=1$
$\therefore P(E\cap F)=\frac{1}{52}P(E\cup F)=P\left(E\right)+P\left(F\right)-P(E\cap F)\Rightarrow P(E\cup F)=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{4}{13}$
Therefore, probability that the card will be a club or a king
$=\frac{4}{13}$