# A card is drawn randomly from a standard deck of cards. Determine

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

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) = $$\frac{1}{4} + \frac{1}{13} – \frac{1}{52} = \frac{16}{52} = \frac{4}{13}$$.