Question

One card is drawn from a pack of $52$ cards. The probability that the card picked is either a spade or a king.

• A. $\frac{1}{26}$
• B. $\frac{3}{26}$
• C. $\frac{4}{13}$
• D. $\frac{1}{9}$

Answer 1

Answer: (C)

$\frac{4}{13}$

Let $A:$ event of drawing a king

$\Rightarrow P\left(A\right)=\frac{4}{52}=\frac{1}{13}$

$B:$ event of drawing a spade $=\frac{13}{52}=\frac{1}{4}$

$\Rightarrow P(A\cap B)=\frac{1}{52}$

$\therefore P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=\frac{1}{13}+\frac{1}{4}-\frac{1}{52}=\frac{4}{13}$