Question

Suppose you ask someone to say a two-digit number.

(i)

What is the probability of this number having both digits the same?

(ii)

What is the probability of the first digit being larger than the second?

(iii)

What is the probability of the first digit being smaller than the second?

Answer 1

The numbers ranging from 10 to 99 can be termed as two digit numbers, so there are 90 numbers which have two digits.

(i)

The two digit numbers which have their both the digits as same are 11, 22, 33, 44, 55, 66, 77, 88 and 99.

There are nine numbers of this type.

Probability of obtaining such a number =

∴Probability of obtaining a two digit number which has its both the digits as same =

(ii)

The two digit numbers which have their first digit larger than the second digit are 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97 and 98.

The total number of such type of numbers is 45.

Probability of obtaining such a number =

∴Probability of obtaining a two digit number which has its first digit larger than the second digit =

(iii)

The two digit numbers which have their first digit smaller than the second digit are 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79 and 89.

The total number of such type of numbers is 36.

Probability of obtaining such a number =

∴Probability of obtaining a two digit number which has its first digit smaller than the second digit =