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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.

Respuesta :

Answer: Probability of winning a small prize is [tex]\dfrac{9}{13}[/tex]

Step-by-step 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) [tex]=\dfrac{3}{4}\times \dfrac{12}{13}\\\\=\dfrac{36}{52}\\\\=\dfrac{18}{26}\\\\=\dfrac{9}{13}[/tex]

Hence, probability of winning a small prize is [tex]\dfrac{9}{13}[/tex]

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