Question

One ticket is selected at random from $100$ tickets numbered $00,01,02,...,99$. Suppose $S$ and $T$ are the sum and product of the digits of the number on the ticket, then the probability of getting $S=9$ and $T=0$ is

• A. $\frac{19}{100}$
• B. $\frac{1}{4}$
• C. $\frac{2}{19}$
• D. $\frac{1}{50}$

Answer 1

The correct option is D $\frac{1}{50}$

We have $(S=9)=\{09,18,27,36,45,54,63,72,81,90\}$
and $(T=0)=\{0,01,...,09,10,20,...,90\}$
Also $(S=9)\cap (T=0)=\{09,90\}$
Thus $P((S=9)\cap (T=0))=\frac{2}{100}$