One Ticket Is Selected At Random From 50 Tickets Numbered 00,01,02,03,............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

Any number in the set S={00,01,02…..,49} is of the form ab.

where a ∈ {0,1,2,3,4} and b ∈ {0,1,2,…..,9}

For the product of digits to be zero, the number must be of the form either x0, which are 5 in numbers, because x ∈{0,1,2,3,4}

The form 0x, which are 10 in numbers because x∈{0,1,2,…..,9}

The only number common to both is = 00.

Thus the number of numbers in S, the product of whose digits is zero =10+5−1=14.

The number whose sum of digits is 8 is just one, i.e. 08

The required probability =1/14.

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