Question

Two cards are drawn simultaneously (without replacement) from a well-shuffled pack of $52$ cards. Find the mean and variance of the number of red cards.

• A. Mean $=0.1$ and Variance $=0.7$
• B. Mean $=0.6$ and Variance $=0.3$
• C. Mean $=0.49$ and Variance $=0.37$
• D. Mean $=0$ and Variance $=0.45$

Answer 1

The correct option is C Mean $=0.49$ and Variance $=0.37$

Since we have to draw two red cards(without replacement) from $52$ cards, therefore the probability is:

$p=\frac{26}{52}\times \frac{25}{51}=\frac{25}{102}$

And, $q=1-\frac{25}{102}=\frac{77}{102}$

Since $n=2$, therefore,

$Mean=np=2\times \frac{25}{102}=\frac{50}{102}=0.49$

$Variance=npq=2\times \frac{25}{102}\times \frac{77}{102}=0.37$