Question

One card is drawn from a pack of 52 cards. The probability that it is the card of a king or spade is

Options

•  1/26

• 3/26

•  4/13

•  3/13

   

Answer 1

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