What is the probability of being dealt 4 hearts from a standard 52-card deck if only 4 cards are to be dealt?

What is the probability of being dealt 4 hearts from a standard 52-card deck if only 4 cards are to be dealt?

• A. 11/4165
• B. 1/13
• C. 1/270725
• D. 13/52

Answer: (A)

When drawing four cards from a standard deck without replacement, the event we want is that all four cards are hearts. There are 13 hearts in the deck, so the number of favorable hands is choosing 4 hearts from 13: C(13,4) = 715. The total number of possible 4-card hands from 52 cards is C(52,4) = 270,725. So the probability is 715/270,725, which simplifies to 11/4165. You can also see this by multiplying sequentially: (13/52) × (12/51) × (11/50) × (10/49), which yields the same result. The exact probability is 11/4165 (about 0.264%).

When drawing four cards from a standard deck without replacement, the event we want is that all four cards are hearts. There are 13 hearts in the deck, so the number of favorable hands is choosing 4 hearts from 13: C(13,4) = 715. The total number of possible 4-card hands from 52 cards is C(52,4) = 270,725. So the probability is 715/270,725, which simplifies to 11/4165. You can also see this by multiplying sequentially: (13/52) × (12/51) × (11/50) × (10/49), which yields the same result. The exact probability is 11/4165 (about 0.264%).