Question

A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.

Answer 1

If A and B denote the events of drawing an ace 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, i.e. an ace 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)
= $\frac{4}{52}+\frac{13}{52}-\frac{1}{52}=\frac{4+13-1}{52}=\frac{16}{52}=\frac{4}{13}$
Hence, the probability that the card drawn is either an ace or a spade card is given by $\frac{4}{13}.$