One ticket is selected at ransom form 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, is

Options

A. `(1)/(14)`
B. `(1)/(7)`
C. `(5)/(14)`
D. `(1)/(50)`

Answer

A

Explanation

Consider the following events :
A=Sum of the digits on the selected ticket is 8.
B= Product of the digits on the selected ticket is zero.
There are 14 tickets having product of digits appearing on them as zero. The numbers on such tickets are 00, 01, 03, 04, 05, 06, 07, 08, 09, 10, 20, 30,40.
`therefore P(B)=(14)/(50) " and " P(A cap B)=(1)/(50)`
Required probability `=P(A//B)=(P(A cap B))/(P(B))=(1)/(4)`