Question

Suppose that you draw 2 cards without replacement from a standard 52-cards deck. What is theprobability that all cards are aces? It is unusual probability. Write your answer with three decimal places

Answer 1

Answer:

1/221 or 0.005

Explanation:

• The number of aces in a standard 52-cards deck = 4

,

• The total number of cards = 52

The probability of drawing two cards (Aces) without replacement is given below:

$\begin{gathered} P(1st\text{ Ace)}=\frac{4}{52} \\ P(2nd\; \text{Ace)}=\frac{3}{51} \end{gathered}$

Therefore, the probability that all cards are aces is:

$\begin{gathered} P(\text{all aces)}=\frac{4}{52}\times\frac{3}{51}=\frac{1}{221} \\ \approx0.005 \end{gathered}$

The probability is 1/221 (as a fraction) and 0.005 (as a decimal correct to 3 decimal places).