# In Exercises 5–36, express all probabilities as 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?

Question
1 views

In Exercises 5–36, express all probabilities as 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?

check_circle

Step 1

There are 10 possible ways for selecting of each digit for ATM pin, they are,

.

Multiplication counting rule:

In a sequence of events, for which first event appears in n1 number of ways, second event appears in n2 number of ways and so on till nth  event appears in nn number of ways, the total number of outcomes is given by the multiplication rule.

Step 2

The ATM pin code consists of 4 digits, that is the number of possible ways for ATM pin is,

There would be only one correct ATM pin number out of 10,000 possible ways.

Let event A denote correct ATM pin number in the first attempt.

Probability:

The formula for probability of event A is,

Step 3

Substitute 1 for ‘Number of ways of event A occurs’ a...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in