## 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