One ticket is selected at random from 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, equals

Options

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

Answer

A

Explanation

`S={00,01,02,…,49}`
Let A be the event that sum of the digits on the selected ticket is 8, then `A = {08, 17, 26, 35, 44}`. Let B be the event that the product of the digits is zero, then
`B = {00,01,02,03,…,09,10,20,30,40} rArr A nn B ={08}`
`therefore` Required probability `=P((A)/(B))=(P(A nn B))/(P(B))=(1//50)/(14//50)=(1)/(14)`