Question

Numbers $1,2,3,...,2n(n\in N)$ are printed on $2n$ cards. The probability of drawing a number $n$ is proportional to $r$. Then the probability of drawing an even number in one draw is

• A. $\frac{n+2}{n+3}$
• B. $\frac{n+1}{n+3}$
• C. $\frac{1}{2}$
• D. $\frac{n+1}{2n+1}$

Answer 1

Answer: (D)

If $P(r)$ is the probability that the number $r$ is drawn in one draw, it is given that $P(r)=kr$, where $k$ is a constant.
Further $P(1)+P(2)+....+P(2n)=1$
$\Rightarrow k(1+2+3+...+2n)=1$
$\Rightarrow k=\frac{1}{n(2n+1)}$
Hence the required probability
$=P(2)+P(4)+P(6)+....+P(2n)$
$=2k(1+2+...+n)$
$=\frac{2}{n(2n+1)}\cdot \frac{n(n+1)}{2}$
$=\frac{n+1}{2n+1}$