One is asked to s

Total number of two -digit numbers = 90

i. Probability of both digits being the same

Total number of numbers having same digit = 9

Probability of both digits being same

= 0.10

ii. Probability of first digit being larger

Total number of numbers having first digit larger = 45

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, 98.

Probability of first digit being larger

= 0.50

iii. Probability of first digit being smaller

Total number of numbers having first digit smaller = 36

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, 89.

Probability of first digit being smaller

= 0.25