Question

Three cards are drawn one by one from a deck of $52$ playing cards without replacement. What is the probability of getting a King then an Ace and then a two?

• A. $\frac{4}{52}\times \frac{4}{51}\times \frac{2}{50}$
• B. $\frac{1}{13}\times \frac{4}{51}\times \frac{2}{25}$
• C. $\frac{1}{13}\times \frac{1}{51}\times \frac{1}{50}$
• D. All of the above.

Answer 1

The correct option is B $\frac{1}{13}\times \frac{4}{51}\times \frac{2}{25}$

Given, three cards are drawn from a deck having $52$ cards without replacement.

Also, in a deck each kind of cards are $4$ in numbers.

Let $\text{A},$ $\text{B},$ and $\text{C}$ be three events of drawing first a King, second an Ace, and third a two respectively without replacement.

Probability of choosing a King first is $\text{P(A)}=\frac{4}{52}=\frac{1}{13}$

Probability of choosing an Ace is $\text{P(B)}=\frac{4}{51}$

Probability of choosing a two is $\text{P(C)}=\frac{4}{50}=\frac{2}{25}$

We have to find the probability of getting a King then an Ace and then a two which is equal to $\text{P(E)}.$

$\Rightarrow \text{P(E)}=\text{P(A)}\times \text{P(B)}\times \text{P(C)}$

$\Rightarrow \text{P(E)}=\frac{1}{13}\times \frac{4}{51}\times \frac{2}{25}$