Question

A passcode to enter a building is a sequence of 4 single digit numbers (0-9), and repeated digits aren'tallowed.Suppose someone doesn't know the passcode and randomly guesses a sequence of 4 digits.What is the probability that they guess the correct sequence?

Answer 1

0.0001984

Step-by-step explanation

There are 10 possible values for each digit of the passcode to enter the building.

These include: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

So, there are:10 x 10 x 10 x 10 = 10^4 = 10,000 total possible passcodes.

For no repeat passcode

We have: 10 x 9x 8 x7 = 5040 total possible passcodes without repetition.

Probability of guessing correct sequence

Since there is only 1 correct sequence of 4 digits passcode (without repetition) to enter the building

`\begin{gathered} Prob\text{ = }(1)/(5040) \\ Prob\text{ = 0.0001984} \end{gathered}`

Hence, the probability that they guess the correct sequence is 0.0001984