Question

3 digits are drawn independently and at random to obtain a 3-digit number. Each of the 3 digits can take integer values 1 through 9, with each integer being equally likely to be chosen. In other words, the 3-digit number can be from 111 through 999, but any 3-digit number that contains 0 is impossible.

A. What is the chance that the 3-digit number is even?

B. What is the chance that the 3-digit number has at least one digit that is a 1?

C. What is the chance that all three digits in the 3-digit number are the same?

Answer 1

total number of digits =N(9 choices for each) =9*9*9 =729

a)

number of ways digit is even =N(9 choice for 1st two digit and 4 (Even numbers for 3rd)=9*9*4=324

chance that the 3-digit number is even=(324/729)*100 =44.44%

b)

number of ways at least one digit is 1 =total ways -N(none is 1) =9^3-8^3=217
chance that the 3-digit number has at least one digit that is a 1=(217/729)*100 =29.77%

c)

chance that all three digits in the 3-digit number are the same =(9/729)*100 =1.23 %