Question

A card is randomly drawn from a standard $52$-card deck. An ace of hearts wins the grand prize; any other ace or heart wins a small prize. What is the probability of winning a small prize? Express your answer as a common fraction. Assume that a grand prize winner does NOT also win a small prize.

Answer 1

Answer: Probability of winning a small prize is
`(9)/(13)`

Explanation:

Since we have given that

Number of cards in a deck = 52

Grand prize for an ace of heart

Small prize for any other ace or heart.

We need to find the probability of winning a small prize.

P(winning a small prize) = P(any other ace) × P(heart)

P(winning a small prize)
`=(3)/(4)* (12)/(13)\\\\=(36)/(52)\\\\=(18)/(26)\\\\=(9)/(13)`

Hence, probability of winning a small prize is
`(9)/(13)`