Question

A bag contains n cards numbered as 1 , 2 , 3 ,....... upto n, well mixed up. A person 'P' draws a card from the bag and puts it back in the bag. Then a person 'Q' draws a card from the bag. The odds in favour of P getting a card with higher number than Q is :

• A. n -1 : n + 1
• B. n : n -1
• C. n + 1 : n
• D. (n + 1) : (n -1)

Answer 1

Answer: (A)

$S=\{n,(n-1),(n-2),\dots \dots ..3,2,1\}$
suppose ' $P$ ' draws the card number ' $n$ ' the probability of which is $\frac{1}{n}$
' $P^{\prime }$ draws a higher number than ' $Q$ ' $=\frac{1}{n^2}[(n-1)+(n-2)+\dots .+1]$
$=\frac{(n-1)n}{2n^2}=\frac{n-1}{2n}=\frac{n-1}{(n-1)+n+1}$
$\Rightarrow$ odds in favour $=(n-1):(n+1)\Rightarrow (A)$