Question

Use the method of your choice to determine the following probability.Drawing three 9s in a row from a standard deck of cards when the drawn card is not returned to the deck each time.

Answer 1

Answer:

1/5525

Explanation:

In a standard deck of cards, there are a total of 52 cards.

There are 4 cards labeled 9.

Since the draw is without replacement, the total number of cards reduces after each draw. Therefore:

$\begin{gathered} P(\text{picking the first 9)}=\frac{4}{52} \\ P(\text{picking the second 9)}=\frac{3}{51} \\ P(\text{picking the third 9)}=\frac{2}{50} \end{gathered}$

Thus, the probability of drawing three 9s in a row is:

$P(\text{thre}e\text{ 9s)}=\frac{4}{52}\times\frac{3}{51}\times\frac{2}{50}=\frac{1}{5525}$

The probability is 1/5525.