Question

Avery sets up a passcode on her tablet, which allows only 9 digit codes. A spy sneaks a look at Avery’s tablet and sees her fingerprints on the screen over nine numbers. What is the probability the spy is able to unlock the tablet on his first try? Express your answer as a fraction.

Answer 1

The probability of the spy unlocking the tablet on his first try is 1 in 10^9.

Step-by-step explanation:

To calculate the probability of the spy unlocking the tablet on his first try, we need to determine the number of possible combinations of 9-digit passcodes. Each digit can take on values from 0 to 9, so there are a total of 10 possible options for each digit.

Since there are 9 digits, the total number of combinations is 10^9. Therefore, the probability of the spy unlocking the tablet on his first try is 1 out of 10^9.

Expressed as a fraction, the probability is 1/10^9.

Answer 2

We will have the following:

Since the spy sees fingerprints in 9 digits, then she used 9 different numbers for the password, so the posibility will be the following:

`P=(1)/(10)\cdot(1)/(9)\cdot(1)/(8)\cdot(1)/(7)\cdot(1)/(6)\cdot(1)/(5)\cdot(1)/(4)\cdot(1)/(3)\cdot(1)/(2)\Rightarrow P=(1)/(5443200)`