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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.

Respuesta :

youngevanevan

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

LucianoBordoli

Answer:

Carmen's prediction is low because 200 times [tex]\frac{1}{4}[/tex] is 50.

Step-by-step 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 [tex]P(A)=\frac{2}{8}=\frac{1}{4}[/tex]

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,[tex]\frac{1}{4}[/tex])

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

[tex]E(X)=np=200.\frac{1}{4}=50[/tex]

We answer that Carmen's prediction is low because 200 times [tex]\frac{1}{4}[/tex] is 50.

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