Question

There are n cards in a pack numbered from 1 to n. A and B are two individuals who draw a card from the pack. Find the probability that the card drawn by A is higher than that drawn by B.

A

• A. $\frac{1}{n}$
• B. $\frac{n-1}{2n}$
• C. $\frac{n+1}{2n}$
• D. $\frac{n-1}{n}$

Answer 1

The correct option is B $\frac{n-1}{2n}$

P(card drawn by $A$ greater than $B$)

= P($B$ draws card $1$)$\times$P($A$ draws any card $>1$) $+$ P($B$ draws card $2$)$\times$P($A$ draws any card $>2$) $+$ ...... $+$P($B$ draws card $n-1$)$\times$P($A$ draws any card $>n-1$)

$=\frac{1}{n}\times \frac{n-1}{n}+\frac{1}{n}\times \frac{n-2}{n}+\frac{1}{n}\times \frac{n-3}{n}+....+\frac{1}{n}\times \frac{1}{n}$

$=\frac{1}{n}\times \frac{(n-1)n}{2n}=\frac{n-1}{2n}$