Question

One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. What is the probability that the card drawn is either a red or a king?

• A. $\frac{7}{13}$
• B. $\frac{1}{13}$
• C. $\frac{27}{52}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{7}{13}$

Out of the 52 cards, one card can be drawn in 52 ways. The total number of elementary events = 52.
There are 26 red cards and 4 king cards. However, two of the king cards are also red. They are being counted twice, once in the red cards set and once in the king set. We need to count them only once, say in the king cards set. So we don't count them in the red cards set. Thus the number of red cards reduces to 24.
Total number of favourable outcomes = 24+4 = 28.
Out of this 1 card can be drawn in 28 ways.
$\therefore$ Required probability $=\frac{28}{52}=\frac{7}{13}$