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 find the probability of X= 9 and Y=0.

• A. $P\left(X\right)=\frac{2}{19},P\left(Y\right)=\frac{1}{10}$
• B. $P\left(X\right)=\frac{9}{50},P\left(Y\right)=\frac{1}{10}$
• C. $P\left(X\right)=\frac{1}{10},P\left(Y\right)=\frac{9}{50}$
• D. $P\left(X\right)=\frac{1}{12},P\left(Y\right)=\frac{9}{50}$

Answer 1

The correct option is C $P\left(X\right)=\frac{1}{10},P\left(Y\right)=\frac{9}{50}$

$N\left(s\right)=100$
$Y=\{00,01,02,03,04,05,06,07,08,09,10,20,30,40,50,60,70,80,90\}N\left(Y\right)=18P\left(Y\right)=\frac{N\left(Y\right)}{N\left(s\right)}=\frac{18}{100}=\frac{9}{50}X=\{09,18,27,36,45,54,63,72,81,90\}N\left(X\right)=10P\left(X\right)=\frac{N\left(X\right)}{N\left(s\right)}=\frac{10}{100}=\frac{1}{10}\therefore \text{The probability of X is}\frac{1}{10}\text{and Y is}\frac{9}{50}$