First slide

Introduction to probability

Question

A three-digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three digits same is

Moderate

A

$\frac{1}{9}$
B

$\frac{1}{10}$
C

$\frac{1}{50}$
D

$\frac{1}{100}$

Solution

Three-digit numbers are 100, 101, ..., 999. Total number of such numbers is 900.
. The three-digit numbers (which have all same digits) are 111, 222, 333, ..., 999.
Favorable number of cases is 9. Therefore, the required probability is $\frac{9}{900} = \frac{1}{100}$

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