Answer:
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%
