Question

One ticket is selected at random from $100$ tickets numbered $00,01,02,...,99$. Suppose $X$ and $Y$ are the sum and product of the digits found on the tickets $P(X=7;Y=0)$ is given by

• A. $\frac{2}{3}$
• B. $\frac{2}{19}$
• C. $\frac{1}{50}$
• D. None of these

Answer 1

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

We have $(X=7)=\{07,16,25,34,43,52,61,70\}$

and $(Y=0)=\{00,01,02,...,10,20,30,..,90\}$

Thus $(X=7)\cap (Y=0)=\{07,70\}$

$\therefore P(X=7;Y=0)=\frac{2}{100}=\frac{1}{50}$