Question

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

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

Answer 1

The correct option is C

$\frac{4}{13}$

If A and B denote the events of drawing a king and a spade card, respectively, then event A consists of four sample points,
whereas evebt B consists of 13 sample points.

Thus, $P\left(A\right)=\frac{4}{52}$ and $P\left(B\right)=\frac{13}{52}$

The compound event $(A\cap B)$ consists of only one sample point, king of spade

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

By addition theorem, we have

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=\frac{4}{52}=\frac{13}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$