Kiara sets up a passcode on her smart phone, which allows only eight-digit codes.
A spy sneaks a look at Kiara’s smart phone and sees her fingerprints on the screen over eight numbers.
What is the probability the spy is able to unlock the smart phone on his first try? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Probabilities are used to determine the chances of events
The probability the spy is able to unlock the smart phone on his first try is 0.00000001
How to determine the probability
The length of the password is given as:
L = 8
Each of the digit in the password can take any of digits 0 – 9 (i.e. 10 digits)
So, the number of possible password is:
The probability that the spy unlocks the phone is:
So, we have:
Hence, the probability the spy is able to unlock the smart phone on his first try is 0.00000001