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Question: One ticket is selected at random from 100 tickets numbered 00, 01, 02,..., 98, 99. If X and Y denote...

One ticket is selected at random from 100 tickets numbered 00, 01, 02,..., 98, 99. If X and Y denote the sum and the product of the digits on the tickets, then P(X=9/Y=0) equals

A

1/19

B

2/19

C

3/19

D

None of these

Answer

2/19

Explanation

Solution

Event (Y = 0) is {00, 01, 09, 10, 20,...90}

Also (X = 9)∩(Y=0) = 09.90, we have P(Y=0) = 19100\frac{19}{100}

and P(X=9)∩(Y=0) = 2100\frac{2}{100}.

Hence required probability

= P{(X = 9)/(Y=0)} = {P(X=9)∩(Y=0)}P(Y=0)=219\frac{\{ P(X = 9) \cap (Y = 0)\}}{P(Y = 0)} = \frac{2}{19}