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?

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Expert Answer

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.

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Total number of outcomes =n, x n, x...Xn,

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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,

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Number of ways event A occurs Number of simple events P(A)=

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Step 3

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

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P(4)= 10,000

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