The NAU student ID number is a 9digit number Assume all numb

The NAU student ID number is a 9-digit number. Assume all numbers are randomly generated, and all numbers are equally likely to be generated. a) How many possible student ID numbers are there? b) What is the probability of getting the ID number that is all 1s, 111111111? c) How many student ID numbers have a 1 as the first digit? d) What is the probability of getting a student ID number with a 1 as the first digit?

Solution

a) Because the student ID is a 9 digit number, it can range from 100000000 to 999999999. So number of possible student ID numbers = 900000000 .

b) Probability of getting the ID number as 111111111 = 1/900000000 .

c) Having 9 digits and with 1 as first digit, the student ID can range from 100000000 to 199999999. So the number of possible student ID numbers in this case = 100000000 .

d) Probability of getting a student ID number with 1 as first digit =100000000/900000000=1/9 = 0.1111