Question

From a well shuffled deck of cards, $2$ cards are drawn with replacement. If $x$ represent numbers 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

$\frac{25}{169}$

Explanation for the correct option:

Find the value of $P(x=1)+P(x=2)$:

Let $X$ be the random variable for number of aces

$\because X$ takes the values $0$(chances of getting no aces), $1$(chances of getting one ace), $2$(chances of getting two aces)

Now, Chances of getting no aces, $P(X=0)=\frac{48}{52}\times \frac{48}{52}$

$=\frac{144}{169}$

$\therefore P(X=1)+P(X=2)=1-P(X=0)$ $\left[\mathbf{\because }\mathit{P}\mathbf{\left(}\mathit{E}\mathbf{\right)}\mathbf{+}\mathit{P}\mathbf{\text{'}}\mathbf{\left(}\mathit{E}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\right]$

$=1-\frac{144}{169}$

$=\frac{\mathbf{25}}{\mathbf{169}}$

Hence, Option ‘A’ is Correct.