JEE Main 2009 — Probability & Statistics

If the mean deviation of number $1,1+d, 1+2 d, \ldots ., 1+100 d$ from their mean is 255 , then the $d$ is equal to

Statement-1 : The variance of first $n$ even natural numbers is $\frac{n^2-1}{4}$ Statement-2 : The sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n(n+1)(2 n+1)}{6}$

One ticket is selected at random from 50 tickets numbered $00,01,02, \ldots, 49$. Then the probability that the sum of the digits on the selected ticket is 8 , given that the product of these digits is zero, equals