Question

A thief steals an ATM card and must randomly guess the correct five​-digit pin code from a 7​-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first​ try?

Answer 1

Answer:

1 in 16,807 chance or a 0.00595% chance

Step-by-step explanation:

There is only one correct 5-digit pin that the thief must guess. If there are 7 possible values for each of the five digits, the total number of combinations is:

$n = 7*7*7*7*7\\n= 16,807\ possibilities$

Therefore, there is a 1 in 16,807 chance or a 0.00595% chance that the thief will guess on the first try.