Question

You have a deck of 52 cards. What’s the probability you draw exactly 1 heart in 2 draws with replacement?

Answer 1

Answer:  The required probability is $\dfrac{3}{16}.$

Step-by-step explanation:  Given a deck of 52 cards.

We are to find the probability of drawing exactly 1 heart in 2 draws with replacement.

Number of hearts in the deck = 13.

Let S be the sample space of drawing two cards from the deck of 52 cards and E denote the event of drawing exactly 1 heart in 2 draws with replacement.

Then,

$n(S)=^{52}C_1\times^{52}C_1=52\times52,\\\\\\n(E)=^{13}C_1\times^{52-13}C_1=13\times39.$

Therefore, the probability of event E is

$P(E)=\dfrac{n(E)}{n(S)}=\dfrac{13\times39}{52\times52}=\dfrac{1\times3}{4\times4}=\dfrac{3}{16}.$

Thus, the required probability is $\dfrac{3}{16}.$

Answer 2

Answer: The probability you draw exactly 1 heart in 2 draws with replacement is 3/16

Step-by-step explanation:

The probability of picking a heart in a pack of 52 playing card is

13/52=1/4

The probability of drawing exactly one heart in 2 draws with replacement mean;

That the first draw is a heart and the second draw is not a heart

The probability that the second draw is not a heart is= 1-1/4= 3/4

Therefore

The probability you draw exactly 1 heart in 2 draws with replacement is

1/4 * 3/4 = 3/16