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?

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%