Question

$A$ draws a card from a pack of $n$ cards marked $1,2,....,n$. The card is replaced in the pack and $B$ draws a card.

Find the probability that $A$ draws the same card as $B$.

• A. $1/n$
• B. $1/(n-1)$
• C. $1/(n+1)$
• D. $2/n$

Answer 1

The correct option is A $1/n$

$n\left(S\right)=n$
$A$ can draw $1$ card from $1,2,3,\mathrm{4...}n$ in ${}^n{C}_1$ ways
But $B$ can draw that same card in only $1$ way
Therefore required probability $=\frac{1}{n}$