Question

From a well shuffled deck of cards, $2$ cards are drawn with replacement. If $x$ represent number of times ace coming, then value of $P(x=1)+P(x=2)$ is

• A. $\frac{25}{169}$
• B. $\frac{24}{169}$
• C. $\frac{49}{169}$
• D. $\frac{23}{169}$

Answer 1

The correct option is A $\frac{25}{169}$

Let $X$ be the random variable denoting the number of aces when $2$ cards are drawn, with replacement from a well-shuffled pack of $52$ cards.

$X$ takes the values $0,1,2$.

Now,

$P(X=0)=\frac{48}{52}\times \frac{48}{52}=\frac{144}{169}$

Therefore,

$P(X=1)+P(X=2)=1-P(X=0)=1-\frac{144}{169}=\frac{25}{169}$