Q2 of 18 Page 76

One is asked to say a two-digit number.

i) What is the probability of both digits being the same?


ii) What is the probability of the first digit being larger?


iii) What is the probability of the first digit being smaller?

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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