Question

Two cards are pulled in order from a deck of 52 playing cards. What is the probability that thecards will be an 8 of hearts and then an Ace?

Answer 1

ANSWER

$\frac{1}{663}$

EXPLANATION

The probability that an 8 of hearts and then an ace is drawn can be calculated by finding the product of the probability of drawing an 8 of hearts and an ace (after the 8 of hearts has been drawn)

There is only one 8 of hearts in a deck of cards, so the probability of drawing an 8 of hearts is:

$P(8-of-hearts)=\frac{1}{52}$

After the 8 of hearts is drawn, only 51 cards will remain. There are four aces (for each of the 4 suits), therefore, the probability of drawing an ace is:

$P(ace)=\frac{4}{51}$

Therefore, the probability that an 8 of hearts and then an ace is drawn is:

$\begin{gathered} \frac{1}{52}\cdot\frac{4}{51} \\ \Rightarrow\frac{1}{663} \end{gathered}$