Question

Michelle 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?
A)



1
16



B)



1
26



C)



1
4



D)



1
52

 these are fractions

Answer 1

The answer is A. The probability that you draw hearts than spades is 1/16 If drawing more than one card with replacement: The probability of drawing a specific card each time is 1/52n n= the number of draws. The probability of drawing a specific card each time is 1/13n. The probability of drawing a specific suit each time is 1/4n. Since you draw two types of cards,each time you drew is 1/4 so 1/4 times 1/4 is 1/16. Kind of cofusion right

Answer 2

Answer:

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

Step-by-step explanation:

Michelle draws a card from a standard deck of 52 cards.

It means sample taken n(S) = 52

When she draws a card which is a heart the favorable event n(E) = 13

Therefore probability of drawing a heart will be P1 = $\frac{n(E)}{n(S)}=\frac{13}{52}=\frac{1}{4}$

She replaces this card and draws again. Therefore the probability of drawing second card which will be a spade will be P2 = $\frac{13}{52}=\frac{1}{4}$

Now probability that she draws a heart and then a spade will be = $P_{1}.P_{2}=\frac{1}{4}.\frac{1}{4}=\frac{1}{16}$

Option A. $\frac{1}{16}$  is the correct option.