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StatisticsQ&A LibraryIn 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

Asked Dec 22, 2019

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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?

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 *n*_{1} number of ways, second event appears in *n*_{2} number of ways and so on till *n*^{th} event appears in *n*_{n} 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...

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