Question

One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that.

1. The card drawn is black.

2. The card drawn is a king.

3. The card drawn is black and a king.

The card drawn is either black or a king.

Answer 1

1. A pack of 52 cards has 26 black cards. So one black card may be drawn in 26 ways. Therefore; Probability of card drawn is black

= \(\frac{26}{52} = \frac{1}{2}\)

2. A pack of 52 cards has 4 kings. So one king card may be drawn in 4 ways. Therefore; Probability of drawing a king

= \(\frac{4}{52} = \frac{1}{13}\)

3. A pack of 52 cards has 2 black king cards. So one black king card may be drawn in 2 ways. Therefore; Probability of drawing a king

= \(\frac{2}{52} = \frac{1}{26}\)

4. A pack of 52 cards has 26 black cards which include 2 black king and 2 red king cards. So number of cards which are black or king cards.

= 26 + 2 = 28.

Therefore; Probability of drawing either a black or king card =\(\frac{28}{52} = \frac{7}{13}\).