You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck
is shumed, and you draw agaln. Find the probability of drawing an elght the first time and a
heart the second time.
The probability of drawing an eight the first time and a heart the second time is
(Type an integer or a simplified fraction.)

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UpStudy AI · Accepted Answer

1. There are 4 eights in a 52-card deck. Thus, the probability of drawing an eight on the first draw is
   $$
   P(\text{eight}) = \frac{4}{52} = \frac{1}{13}.
   $$
2. There are 13 hearts in the deck. Thus, the probability of drawing a heart on the second draw is
   $$
   P(\text{heart}) = \frac{13}{52} = \frac{1}{4}.
   $$
3. Since the card is replaced and the deck is shuffled between draws, the two draws are independent. Therefore, the probability of drawing an eight first and a heart second is the product:
   $$
   P(\text{eight then heart}) = \frac{1}{13} \times \frac{1}{4} = \frac{1}{52}.
   $$

The probability is $$\frac{1}{52}$$.
The probability of drawing an eight first and a heart second is $$\frac{1}{52}$$.

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