Question

One ticket is selected at random from 50 tickets numbered $00,01,02,....,49.$ 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

• A. $\frac{1}{7}$
• B. $\frac{5}{14}$
• C. $\frac{1}{50}$
• D. $\frac{1}{14}$

Answer 1

The correct option is D $\frac{1}{14}$

Any number in the set $S=\{00,01,\mathrm{02.....},49\}$ is of the form $ab$
where $a\in \{0,1,2,3,4\}$ and $b\in \{0,1,2,.....,9\}$ for the product of digits to be zero, the number must be of the form either $x0$ which are $5$ in numbers, because $x\in \{0,1,2,3,4\}$ or of the form $0x$ which are $10$ in numbers because $x\in \{0,1,2,.....,9\}$
The only number common to both $=00$ Thus the number of numbers in $S$, the product of whose digits is zero $=10+5-1=14$ Of these the number whose sum of digits is $8$ is just one,
i.e. $08$
The required probability $=1/14$