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?

Answer 1

Sample space={1,2,3,4,5,6,7,8} = 8 possible outcomes
multiple of 4 ={4,8} = 2 favorable outcomes:

P(4 OR 8) = 2/8 = 1/4
Expected values after 200 rolls:

200 x P(4 or 8) = 200 x 1/4 = 50
The prediction is 50

Answer 2

Answer:

Carmen's prediction is low because 200 times  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

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,)

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

We answer that Carmen's prediction is low because 200 times  is 50.