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 th

Question

2 months ago

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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 th

e 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.

Mathematics

2 answers:

AnnZ [12.3K] · Answer 1 · 2026-03-08T20:31:53+03:00

Answer:

Carmen's estimate is too low, since rolling 200 times $\frac{1}{4}$ results in a total of 50.

Step-by-step explanation:

Initially, we will define the sample space for this scenario.

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

For the event A: "Rolling an 8-sided die to get a multiple of 4"

The probability for event A is $P(A)=\frac{2}{8}=\frac{1}{4}$

This is because there are two multiples of 4 (4 and 8) out of a total of eight numbers (1 through 8).

Next, considering the random variable X: "Total count of multiples of 4 if she rolls an 8-sided die 200 times"

X can be described as following a Binomial distribution.

X ~ Bi (n,p)

X ~ Bi (200, $\frac{1}{4}$ )

Where n is the number of rolls and p is the probability of success, defined as rolling a multiple of 4.

The mean for this variable is

$E(X)=np=200.\frac{1}{4}=50$

Thus, we conclude that Carmen's prediction is low, as rolling 200 times $\frac{1}{4}$ yields 50.

Zina [12.3K] · Answer 2 · 2026-03-08T20:31:38+03:00

Zina [12.3K]2 months ago

3 0

Carmen’s estimate is low since 200 times 1/4 equals 50.