201k views
5 votes
Given a deck of cards, what is the probability of drawing a Spade and (without replacing the first card) drawing a Heart?

1 Answer

3 votes

Final answer:

The probability of drawing a Spade followed by a Heart without replacement from a standard deck is 1/16, calculated by multiplying the individual probabilities of each event.

Step-by-step explanation:

The question asks about the probability of drawing a Spade and then drawing a Heart from a standard deck of 52 playing cards without replacing the first card. The suits in a deck are Spades, Hearts, Diamonds, and Clubs, each with 13 cards.

For the first draw, the probability of drawing a Spade (S) is 13 out of 52. Since the Spade is not replaced, there are now 51 cards left for the second draw.

The probability of drawing a Heart (H) on the second draw is therefore 13 out of 51.

The joint probability of these two events occurring in sequence is the product of their individual probabilities:

(13/52) * (13/51)

This simplifies to 1/4 * 13/51 or 1/4 * 1/4 after cancelation, which equals 1/16.

User Gavilan Comun
by
7.6k points