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One hundred tickets are numbered as 00, 01, 02, -----09, ----99 and one ticket is drawn at random from them. If A is the event of getting 9 as the sum of the numbers on the ticket and B is the event of getting 0 as the product of the numbers on the ticket then $P (A \cap B) =$ ______

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$\frac{19}{100}$

$\frac{10}{100}$

$\frac{2}{100}$

$\frac{1}{100}$

answer is B.

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Detailed Solution

$\begin{array}{l} A = {09, 18, 27, 36, 45, 54, 63, 72, 81, 90} = sum o f numbers i s 9 \\ a n d B = product "0" \\ A \cap B = {09, 90} \Rightarrow n (A \cap B) = 2, n (s) = 100 C_{1} \\ P (A \cap B) = \frac{2}{100} \end{array}$

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