Question

From a standard deck of 52 cards two cards are drawn at random without replacement. What is the probability of getting both Ace?

• A. ${\left(\frac{1}{17}\right)}^2$
• B. ${\left(\frac{1}{13}\right)}^2$
• C. $\frac{1}{221}$
• D. None of the above

Answer 1

The correct option is C $\frac{1}{221}$

Given, two cards are drawn from deck having $52$ cards without replacement.
Also, their are $4$ Aces in a deck.

Let $\text{A}$ and $\text{B}$ be two events of drawing first Ace card and second Ace card respectively.
Probability of choosing first Ace card is $\text{P(A)}=\frac{4}{52}=\frac{1}{13}$
Probability of choosing second Ace card is $\text{P(B)}=\frac{3}{51}=\frac{1}{17}$

We have to calculate the probability of getting both ace card which is equal to $\text{P(E)}.$
$\Rightarrow \text{P(E)}=\text{P(A)}\times \text{P(B)}$
$\Rightarrow \text{P(E)}=\frac{1}{13}\times \frac{1}{17}=\frac{1}{221}.$