Please help Discrete math 2 Select an even 3digit decimal in

Please help. Discrete math

2. Select an even 3-digit decimal integer. What is the exact probability that the integer chosem is divisible by 11?

Solution

Given that we have to select a 3 digit decimal integer.

There are 900 3 digit decimal integers from 100 to 999 under base 10.

Even integers would be exactly half of that i.e. 450 even integers.(3 digits)

Integers divisible by 11 for 3 digits start from 110 and end with 990

i.e. arithmetic series 110, 121, 132,.....990

No of even three digits are 110, 132, ....990

Consider the series with even numbers divisible by 11

If nth digit is 990

then 990 = 110+(n-1) 22

880 = (n-1)22

n-1 = 40 and n = 41.

Hence no of 3 digits (even and divisible by 11) = 41

Total no of 3 digits even = 450

Prob that a random digit chosen is even and divisible by 11 = 41/450 = 0.0911