Question

question 8 of 10
the probability of rolling a 4 on a number cube is $\frac{1}{6}$. if you were to roll the cube 48 times, you would expect to get a 4 around 8 times ($\frac{1}{6}cdot48 = 8$).
you simulate 48 rolls. how many 4s would make you question your model?
a. 6
b. 8
c. 24
d. 10

Explanation:

Step1: Analyze the expected value

The expected number of 4s is \(8\) (since \(\frac{1}{6}\times48 = 8\)). Values close to \(8\) are in line with the model.

Step2: Check each option

• Option A: \(6\) is close to \(8\).
• Option B: \(8\) is the expected value.
• Option C: \(24\) is \(\frac{24}{48}=\frac{1}{2}\) probability, which is very far from the expected \(\frac{1}{6}\) probability.
• Option D: \(10\) is relatively close to \(8\) compared to \(24\).

Answer:

C. 24