Question

Carmen is going to roll an 8-sided die 200 times. She predicts that she will roll a multiple of 4 twenty-five times. Based on the theoretical probability, which best describes Carmen’s prediction?

Carmen’s prediction is exact because 200 times 1/8 is 25.

Carmen’s prediction is low because 200 times 1/4 is 50.

Carmen’s prediction is low because 200 divided by 2 is 100.

Carmen’s prediction is high because200 divided by 25 is 8.

Answer 1

Carmen’s prediction is low because 200* 1/4 = 50.

Answer 2

Carmen's prediction is low because 200 times
`(1)/(4)` is 50.

Explanation:

First of all we are going to define the sample space for this exercise.

The sample space is Ω = {1,2,3,4,5,6,7,8}

Given the event A : ''Roll an 8-sided die an get a multiple of 4''

The probability for the event A is
`P(A)=(2)/(8)=(1)/(4)`

Because they are two numbers (4 and 8) over a total of eight numbers (1,2,3,4,5,6,7,8) that are multiple of 4.

Now, given the random variable X : ''Total of numbers multiples of 4 If she rolls

an 8-sided die 200 times''

X can be modeled as a Binomial random variable.

X ~ Bi (n,p)

X ~ Bi (200,
`(1)/(4)`)

In which n is the total times she rolls the 8-sided die and p is the success probability.We define a success as obtain a number multiple of 4.

The mean for this variable is

`E(X)=np=200.(1)/(4)=50`

We answer that Carmen's prediction is low because 200 times
`(1)/(4)` is 50.