Question

A Social Security number consists of nine digits in a particular​ order, and repetition of digits is allowed. After seeing the last four digits printed on a​ receipt, if you randomly select the other​ digits, what is the probability of getting the correct Social Security number of the person who was given the​ receipt?

Answer 1

Answer:  $\dfrac{1}{100,000}$

Step-by-step explanation:

Given : The total number of digits in number system (0 to 9) = 10

The number of digits in a social security number = 9

After last four digits are printed, the number of digits remaining to print = 9-4=5

Since , repetition of digits is allowed, then the total number of ways to print 5 remaining digits is given by :-

$10\times10\times10\times10\times10=100,000$

Now, the probability of getting the correct Social Security number of the person who was given the​ receipt is given by:-

$\dfrac{\text{Number of correct code}}{\text{Total number of codes}}\\\\=\dfrac{1}{100,000}$