Question

If two cards are drawn simultaneously from the same set, then probability that at least one of them will be the ace of heart is

• A. $\frac{1}{13}$
• B. $\frac{1}{26}$
• C. $\frac{1}{52}$
• D. $\frac{3}{13}$

Answer 1

The correct option is B

$\frac{1}{26}$

Explanation for the correct option:

Finding the probability:

Total number of cards$=52$

Total number of ace of heart$=1$

Since, two cards are drawn simultaneously, such that atleast one of them is ace of heart.

$\therefore$Required probability$=\frac{{}^1{\mathrm{C}}_1\times {}^{51}{\mathrm{C}}_1}{{}^{52}{\mathrm{C}}_2}$

$\begin{array}{rcl}& =& \frac{1\times 51\times 2}{52\times 51}\left\{\because {}^n{C}_r=\frac{n!}{r!\left(n-r\right)!}\right\}\\ & =& \frac{2}{52}\\ & =& \frac{1}{26}\\ & & \end{array}$

Hence, the correct option is B.