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?
the probability is
(type an integer or a simplified fraction.)

Explanation:

Step1: Determine number of unknown digits

A Social - Security number has 9 digits. Since the last 4 digits are known, the number of unknown digits is $9 - 4=5$.

Step2: Calculate number of possibilities for each unknown digit

Each digit can be any of 10 values (0 - 9) as digit repetition is allowed. So for each of the 5 unknown digits, there are 10 possibilities.

Step3: Calculate total number of possible combinations for unknown digits

By the multiplication principle, the total number of possible combinations for the 5 unknown digits is $10\times10\times10\times10\times10 = 10^{5}=100000$.

Step4: Calculate the probability

There is only 1 correct combination. So the probability of getting the correct Social - Security number is $\frac{1}{100000}$.

Answer:

$\frac{1}{100000}$