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.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

step-by-step explanation:

graph using a few selected

x         y

-1       15

0         6

1         2.4

2       0.96