Problem

A thief steals an ATM card and must randomly guess the correct five-digit pin code from a 6-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
The number of possible codes is
(Type an integer or fraction. Simplify your answer.)
The probability that the correct code is given on the first try is
(Type an integer or fraction. Simplify your answer.)

Answer

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Answer

Final Answer: The total number of possible codes is \(\boxed{7776}\). The probability that the correct code is given on the first try is \(\boxed{\frac{1}{7776}}\).

Steps

Step 1 :The first part of the question asks for the total number of possible codes. Since the keypad has 6 keys and repetition is allowed, each of the 5 digits in the pin code can be any of the 6 numbers. Therefore, the total number of possible codes is \(6^5\).

Step 2 :Let's calculate this value. total_codes = \(6^5\) = 7776

Step 3 :The second part of the question asks for the probability of guessing the correct code on the first try. Since there is only one correct code, the probability is \(\frac{1}{6^5}\).

Step 4 :Let's calculate this value. probability = \(\frac{1}{7776}\) = 0.0001286008230452675

Step 5 :Final Answer: The total number of possible codes is \(\boxed{7776}\). The probability that the correct code is given on the first try is \(\boxed{\frac{1}{7776}}\).

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