Question

One ticket is selected at random from 100 tickets numbered 00, 01, 02, ...... 98, 99. If X and Y denote the sum and the product of the digits on the tickets, then P(X=9/Y=0) equals

• A. 1/19
• B. 2/19
• C. 3/19
• D. None of these

Answer 1

The correct option is B 2/19

Event (Y=0) is {00, 01, 09, 10, 20, ........ 90}
Also (X=9) $\cap$ (Y=0) = 09, 90, we have
$P(Y=0)=\frac{90}{100}$ and $P(X=9)\cap (Y=0)=\frac{2}{100}$

Hence required probability
$=P(X=9)(Y=0)=\frac{P(X=9)\cap (Y=0)}{P(Y=0)}=\frac{2}{19}$