Question

One ticket is selected at random from 100 tickets numbered 00, 01, 02, ….., 99. Suppose A and B are the sum and product of the digit found on the ticket, respectively. Then $P\left(\frac{(A=7)}{(B=0)}\right)$ is given by

• A. \(\frac{2}{13})
• B.
• C.
• D.

Answer 1

The correct option is B

The sum of the digits can be 7 in the following ways: 07, 16, 25, 34, 43, 52, 61, 70
$\therefore$ (A = 7) = {07, 16, 25,34, 43, 52, 61, 70} Similarly,
(B = 0) = {00, 01,02, … . , 10, 20, 30, …., 90}
Thus,
$(A=7)\cap (B=0)=09,70$
$\therefore P(A=7)\cap (B=0)=\frac{2}{100},P\left(\right(B=0\left)\right)=\frac{19}{100}$ Hence,
$P(A=7)\cap (B=0)=\frac{\left(P\right(A=7)\cap (B=0\left)\right)}{P(B=0)}=\frac{\frac{2}{100}}{\frac{19}{100}}=\frac{2}{19}$