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11 June, 18:15

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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  1. 11 June, 18:16
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    The probability of the thief guessing correctly the 4-digit PIN code is 1/625, 0.0016 or 0.16%.

    Step-by-step explanation:

    1. Let's review the information given to us to answer the question correctly:

    Digits in the PIN = 4

    Digits in the keypad = 5

    Repetition of digits is allowed

    2. What is the probability of a correct guess on the first try?

    Guessing every digit of the PIN code is an independent event because repetition of digits is allowed. Therefore, we have:

    Guessing of the 1st digit of the PIN code = 1/5

    Guessing of the 2nd digit of the PIN code = 1/5

    Guessing of the 3rd digit of the PIN code = 1/5

    Guessing of the 4th digit of the PIN code = 1/5

    Guessing of the correct four-digit of the PIN code = 1/5 * 1/5 * 1/5 * 1/5

    Guessing of the correct four-digit of the PIN code = 1/625 or 0.0016 or 0.16%
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