Question

In a pack of 52 playing cards, three cards are drawn at random with replacement. What is the probability of getting Jack in all 3 draws?

• A. ${\left(\frac{4}{52}\right)}^2$
• B. ${\left(\frac{1}{13}\right)}^3$
• C. ${\left(\frac{3}{13}\right)}^3$
• D. ${\left(\frac{3}{52}\right)}^3$

Answer 1

The correct option is B ${\left(\frac{1}{13}\right)}^3$

Given,
Total cards in a pack $=52$
Number of jack $=4$

Probability of getting first Jack is $\text{P(A)}=\frac{4}{52}=\frac{1}{13}$

Probability of getting second Jack by replaceing the first is $\text{P(B)}=\frac{4}{52}=\frac{1}{13}$

Probability of getting third Jack by replaceing the second is $\text{P(B)}=\frac{4}{52}=\frac{1}{13}$

Now, we have to find probablity of getting Jack in all $3$ draws with replacement.
$\Rightarrow \text{P(A, B and C)}=\text{P(E)}=\text{P(A)}\times \text{P(B)}\times \text{P(C)}$

$\Rightarrow \text{P(E)}=\frac{1}{13}\times \frac{1}{13}\times \frac{1}{13}={\left(\frac{1}{13}\right)}^3$