QQuestionMathematics
QuestionMathematics
A thief steals an ATM card and must randomly guess the correct four-digit PIN code from a 5 -key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
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Answer
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Step 1
To calculate the probability of a correct guess on the first try, we need to determine the total number of possible four-digit codes and the number of favorable outcomes (the correct code).
Step 2
As repetition is allowed, there are $$5 \times 5 \times 5 \times 5 = 625$$ possible four-digit codes.
Since the keypad has 5 keys, the total number of possibilities for each digit is 5.
Final Answer
The probability of a correct guess on the first try is \frac{1}{625}.
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