Two cards are drawn one after another with replacement from a well-shuffled standard deck of 52 cards. Let X be the number of aces obtained. Find P(X=1)+P(X=2).

Home › MCQs › EEJ MAIN Mathematics › Question #6982

EEJ MAIN Mathematics QUESTION #6982

Question 1

Two cards are drawn one after another with replacement from a well-shuffled standard deck of 52 cards. Let $X$ be the number of aces obtained. Find $P(X=1)+P(X=2)$.

$\dfrac{49}{169}$
$\dfrac{52}{169}$
$\dfrac{24}{169}$
$\dfrac{25}{169}$✔️

Correct Answer Explanation

$p=P(\text{ace})=\dfrac{4}{52}=\dfrac{1}{13}$, $q=\dfrac{12}{13}$. Binomial with $n=2$.

$P(X=1)=\binom{2}{1}\cdot\dfrac{1}{13}\cdot\dfrac{12}{13}=\dfrac{24}{169}$

$P(X=2)=\binom{2}{2}\cdot\left(\dfrac{1}{13}\right)^2=\dfrac{1}{169}$

$P(X=1)+P(X=2)=\dfrac{24}{169}+\dfrac{1}{169}=\dfrac{25}{169}$

More Options