Question

From a standard deck of 52 cards, if you are dealt 7 cards, what is the probability of getting a hand that consists of 2 hearts and 5 spades?

A) 13/1,712
B) 1/33,652
C) 11/1,820
D) 5/26,978

Answer 1

To calculate the probability of getting a hand that consists of 2 hearts and 5 spades out of a standard deck of 52 cards, we need to find the probability of getting 2 hearts and 5 spades separately and then multiply them together. The probability is C) 11/1,820.

Step-by-step explanation:

To calculate the probability of getting a hand that consists of 2 hearts and 5 spades out of a standard deck of 52 cards:

• There are 13 hearts in a deck, so the probability of getting 2 hearts is (13 choose 2) / (52 choose 7).
• There are 13 spades in a deck, so the probability of getting 5 spades is (13 choose 5) / (39 choose 5).
• Since the events of getting hearts and spades are independent, we can multiply these probabilities together to get the probability of getting both: [(13 choose 2) / (52 choose 7)] * [(13 choose 5) / (39 choose 5)].

Simplifying this expression, we get the answer C) 11/1,820.