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 4 are known, there are 9 - 4=5 unknown digits.

Step2: Calculate number of possible combinations for unknown digits

Each of the 5 unknown digits can be any of 10 digits (0 - 9). By the multiplication principle, the total number of possible combinations for the 5 unknown digits is $10\times10\times10\times10\times10 = 10^{5}$.

Step3: Calculate probability

There is only 1 correct combination. The probability $P$ of getting the correct combination is the number of favorable outcomes (1) divided by the number of total outcomes ($10^{5}$). So $P=\frac{1}{10^{5}}=\frac{1}{100000}$.

Answer:

$\frac{1}{100000}$