One ticket is selected at random from 100 tickets numbered 00,01,02,...,98,99. Suppose S and T are the sum and product of the digits of the number on the ticket, then the probability of getting S=9 and T=0 is `2//19` b. `19//100` c. `1//50` d. none of these

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`