Question

A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.

Answer 1

Total number of all possible outcomes= 52
There are 26 red cards (including 2 queens) and apart from these, there are 2 more queens.
Number of cards, each one of which is either a red card or a queen = 26 + 2 = 28
Let E be the event that the card drawn is neither a red card nor a queen.
Then, the number of favourable outcomes = (52 − 28) = 24
∴ P( getting neither a red card nor a queen) = P (E) = $\frac{24}{52}=\frac{6}{13}$