Question

54.
An integer from 10 to 99 (both inclusive) is randomly chosen so that each such integer is equally
likely to be chosen. The probability that atleast one digit of the chosen integer is 6 is



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Answer 1

Question :-

An integer from 10 to 99 (both inclusive) is randomly chosen so that each such integer is equally

likely to be chosen. The probability that atleast one digit of the chosen integer is 6 is

Solution :-

• First we will find the sample space S.
• There are 90 numbers in all from 10 to 99 ( both inclusive).
• So, n(S) = 90.

The numbers from 10 to 99 ( both inclusive) which contain at least one digit 6 are

• The desired set E of the numbers required should have at least on 2 in them. 16,60,61,66,63,64,65,67,68,69, 36,46,56,62,76,86 and 96.

• These are 18 in number. So, n(E) = 17.

• So, the required probability
• n(E)/n(S) = 17/90

Hence the probability the number chosen contains at least one digit that is 2 is 17/90.