Question

One ticket is selected at random from $100$ tickets numbered $100,01,02,....98,99.$ If $x_1$ and $x_2$ denotes the sum and product of the digits on the tickets, then $P\left(\right(x_1=9\left)/\right(x_2=0\left)\right)$ is equal to

• A. $2/19$
• B. $19/100$
• C. $1/50$
• D. none of these

Answer 1

The correct option is A $2/19$

Total number of ways , $n\left(S\right)=100$

Sample space for product of digits equal to zero is = $01,02,03,04,05,06,07,08,09,10,20,30,40,50,60,70,80,90,100$

So,

$n\left(x_2\right)=19$

$P\left(x_2\right)=\frac{19}{100}$

Sample space for sum of digits equal to 9 is =$09,18,27,36,45,54,63,72,81,90$

Now, sample space for the sum and product of the digits on the tickets is =$09,90$

Now $P(x_1\cap x_2)=\frac{2}{100}$

Hence, $P\left(\frac{(x_1=9)}{(x_2=0)}\right)=\frac{P(x_1\cap x_2)}{P\left(x_2\right)}=\frac{\frac{2}{100}}{\frac{19}{100}}=\frac{2}{19}$