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 \[\frac{4}{13} .\]