One ticket is selected at random from 100 tickets numbered 00,01,02,...,98,99. If `x_1, a n dx_2` denotes the sum and product of the digits on the tickets, then `P(x_1=9//x_2=0)` is equal to

Options

A. A.
2
/
19
B. B. 19/100
C. C. 1
/
50
D. D. none of these

Answer

A

Explanation

Let the number selected be xy. Then
`x+y=9,0lex,yle9`
`and xy=0impliesx=0,y=9or y=0,x=9`
`P(x_(1)=9//x_(2)=0)(P(x_(1)=9nnx_(2)=0))/(P(x_(2)=0))`
Now, `P(x_(2)=0)=19/100`
`andP(x_(1)=9nnx_(2)=0)2/100`
`impliesP(x_(1)=9//x_(2)=0)=(2//100)/(19//100)=2/19`