If a fair 5-sided die is rolled 5 times, what is the probability that each possible outcome (1, 2, 3, 4, and 5) will occur exactly once

0.0384

Step-by-step explanation:

Given a fair 5 sided die rolled 5 times.

Numbers on it are 1, 2, 3, 4, 5.

To find:

The probability that each number will occur exactly once.

Solution:

Formula for probability of an event E:

At the first roll of die, any number can occur.

So number of possible outcomes = 5

Total number of possible outcomes = 5

At the second roll of die, any number can occur other than that occurred in first roll.

So number of possible outcomes = 4

Total number of possible outcomes = 5

At the third roll of die, any number can occur other than that occurred in first and second roll.

So number of possible outcomes = 3

Total number of possible outcomes = 5

At the fourth roll of die, any number can occur other than that occurred in first, second and third roll.

So number of possible outcomes = 2

Total number of possible outcomes = 5

At the fifth roll of die, any number can occur other than that occurred in first, second, third and fourth roll.

So number of possible outcomes = 1

Total number of possible outcomes = 5

The required probability will be multiplication of all the five probabilities.

step-by-step explanation: