Kiara sets up a passcode on her smart phone, which allows only eight-digit codes. 

Question

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.

Answer

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:

Simplify

Hence, the probability the spy is able to unlock the smart phone on his first try is 0.00000001

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