In Exercises 5–36, express allprobabilitiesas fractions.

ATM Pin Numbers A thief steals an ATM card and must randomly guess the correct pin code that consists of four digits (each 0 through 9) that must be entered in the correct order. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

The pin for accessing the ATM card consists of four digits from 0 to 9 with the digits that can repeat.

The digits need to be entered in the correct order.

The probability of an event A is calculated using the following formula:

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

The number of total ways to design a pin can be computed using the multiplication rule, multiplying the number of available options at each place of the pin.

Let A be the event of making a correct guess.

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

The total number of ways possible for guessing the ATM pin is given as follows:

$10\times 10\times 10\times 10=10000$

The number of favorable ways to guess the pin in the correct order is 1.

The probability of guessing the correct pin on the first try is computed as follows:

$P\left(A\right)=\frac{1}{10000}$

Therefore, the probability of guessing the correct pin on the first try is $\frac{1}{10000}$.