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