Question

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Answer 1

If A and B denote the events of drawing a spade card and a king, respectively, then event A consists of 13 sample points, whereas event B consists of four sample points.
Thus, $P\left(A\right)=\frac{13}{52}$ and $P\left(B\right)=\frac{4}{52}$
The compound event (A ∩ B) consists of only one sample point, i.e. the 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)
= $\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{13+4-1}{52}=\frac{16}{52}=\frac{4}{13}$
Hence, the probability that the card drawn is either a spade or a king is given by $\frac{4}{13}.$