Question

nichole draws a card from a standard deck of 52 cards. she replaces the card and draws a second card. what is the probability that she draws a heart and then a spade? note: there are 13 each of hearts, spades, clubs, and diamonds. a 1/16 b 1/16 c 1/4 d 1/12

Explanation:

Step1: Probability of drawing a heart

A standard deck has 52 cards, and 13 hearts. So the probability of drawing a heart is $\frac{13}{52}=\frac{1}{4}$.

Step2: Probability of drawing a spade (with replacement)

After replacing the card, the deck is still 52 cards. There are 13 spades, so the probability of drawing a spade is also $\frac{13}{52}=\frac{1}{4}$.

Step3: Probability of both events (heart then spade)

Since the two draws are independent (because of replacement), we multiply the probabilities: $\frac{1}{4} \times \frac{1}{4}=\frac{1}{16}$.

Answer:

A. $\frac{1}{16}$