Answer :

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


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