Question

A card is drawn randomly from a standard deck of cards. Determine the probability that the card drawn is a queen or a heart.

(a) \(\frac{1}{4}\)

(b) \(\frac{13}{56}\)

(c) \(\frac{4}{13}\)

(d) \(\frac{5}{52}\)

I had been asked this question during an interview for a job.

Query is from Discrete Probability topic in division Discrete Probability of Discrete Mathematics

Answer 1

Correct answer is (c) \(\frac{4}{13}\)

Easy explanation: Let M be the event that the card is a queen, and let N be the event that the card is a heart. Then Since there are 13 different ranks of cards in the deck, P(M) = \(\frac{1}{13}\) and since there are 4 suits in the deck, P(N) = \(\frac{1}{4}\). There is only one card that is both a queen and a heart, so P(M ⋂ N) = \(\frac{1}{52}\). Therefore, P(M U N) = \(\frac{1}{4} + \frac{1}{13} – \frac{1}{52} = \frac{16}{52} = \frac{4}{13}\).