Question

Avery sets up a passcode on her smart phone, which allows only seven digit codes. A spy sneaks a look at Avery's smart phone and sees her fingerprints on the screen over seven 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 1

Probability

The passcode consists of 7 (different) numbers.

Each digit of the number comes from the 10 digits available 0 to 9.

If the 7 digits are known, but not their order, we can calculate the number of possible combinations as follows.

Assume the passcode is ABCDEFG and we have the letters in any order, only one of which is correct.

Once one position is known, the other 6 positions can be sorted in a number given by the combinatorial

7*6*5*4*3*2*1 = 5,040

Only one of those combinations is correct, thus the probability of the spy to unlock the phone on his first try is:

P = 1 / 5,040

Expressed as a decimal:

P = 0.000198

To the nearest millionth