Question

In Exercises 5–36, express all probabilities as fractions.

Social Security Numbers 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?

Short answer

The probability of correctly guessing the Social Security Number is equal to$\frac{1}{100000}$.

Step-by-step solution

Given information

The Social Security Number of a person consists of 9 digits.

The number can be formed by the repetition of digits.

The last four digits are seen.

Define probability

The formula for the probability of an event A:

$P\left(A\right)=\frac{\text{Number}\text{of}\text{favorable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

The counts of total and favorable outcomes can be computed by the multiplication rule.

Compute the number of total and favorable outcomes

Let A be the event of making a correct guess.

The number of digits that are required to be guessed is 5.

Given that repetition is allowed, the number of digits available at each place of the sequence is 10.

The total number of ways possible for guessing the first five digits of the Social Security Number is given as follows:

$10\times 10\times 10\times 10\times 10=100000$

The number of favorable ways to guess the correct person corresponding to the number is 1.

Compute the probability

The probability of guessing the correct number is computed as follows:

$P\left(A\right)=\frac{1}{100000}$

Therefore, the probability of guessing the correct number is $P\left(A\right)=\frac{1}{100000}$.