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 (1) 1/14 (2) 1/7 (3) 5/14 (4) 1/50

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 the 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. Than
`B={00,01,02,03,...,09,10,20,30,40}`
`thereforeAnnB={8}`
The required probability is
`P(A//B)=(P(AnnB))/(P(B))`
`=(1/50)/(14/50)=1/14`