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) 1/26
(b) 3/26
(c) 4/13
(d) 3/13

Answer 1

(c) 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 event 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 ∩ B) consists of only one sample point, king of spade.
So, $P\left(A\cap B\right)=\frac{1}{52}$
By addition theorem , we have:
P (A ∪ B) = P(A) + P (B) − P (A ∩ B)
= $\frac{4}{52}+\frac{13}{52}-\frac{1}{52}=\frac{16}{52}=\frac{4}{13}$
Hence, the probability that the card drawn is either a king or a spade is given by $\frac{4}{13}$.