Question

A 5-digit code is given to all cashiers at a store to let them log onto the cash register. What is the probability that an employee receives a code with all 5 numbers the same?

Answer 1

The probability that an employee receives a code with all 5 numbers the same is
`(1)/(10^4)`.

Explanation:

Consider the provided information.

The numbers which we can use in code is: 0,1,2,3,4,5,6,7,8,9

That means there are 10 numbers which we can use.

The total ways of selecting a 5 digit number with all 5 numbers the same = 10.

The total ways of selecting a 5 digit number is: 10×10×10×10×10=
`10^5`

The required probability is:

`Probability=\frac{\text{Favorable outcomes}}{\text{Total number of outcomes}}`

`Probability=(10)/(10^5)`

`Probability=(1)/(10^4)`

Hence, the probability that an employee receives a code with all 5 numbers the same is
`(1)/(10^4)`.