Question

question 3 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 \\(\left(\frac{1}{6} \cdot 48 = 8\
ight)\\).

you simulate 48 rolls. how many 4s would make you question your model?

a. 6
b. 8
c. 10
d. 24

Explanation:

Step1: Understand the model

The model assumes the probability of rolling a 4 is $\frac{1}{6}$, so in 48 rolls, the expected number of 4s is 8.

Step2: Analyze deviations

We question the model when the result is far from the expected value (8). Let's check each option:

• Option A (6): Close to 8 (difference of 2).
• Option B (8): Exactly the expected value.
• Option C (10): Close to 8 (difference of 2).
• Option D (24): Far from 8 (difference of 16), as 24 is half of 48, implying a probability of $\frac{1}{2}$ for rolling a 4, which contradicts the $\frac{1}{6}$ model.

Answer:

D. 24