Question

The probability of rolling a 2 on a number oube is . If you were to roll the cube 30 times, you would expect to get a 2 around 5 times (- 30 (- 30 = 5). You simulate 30 rolls. How many 2s would make you question your model?

A. 5
B. 14
C. 2
D. 8​

Answer 1

In a probability experiment involving rolling a six-sided die 30 times, observing significantly more or fewer 2s than the expected number of 5, such as 14 or 2, could make someone question the fairness of the die or the accuracy of the model.

Step-by-step explanation:

The subject of this question is the probability of getting a certain outcome when rolling a die multiple times. In this case, the student is working with the probability of rolling a 2 on a six-sided die. If you roll a die 30 times, the expected number of times to get a 2 would be around 5, since the probability of rolling a 2 is one-sixth (1/6).

However, in actual experiments, the observed frequency can deviate from the expected frequency due to chance. This is where the concept of a binomial distribution and standard deviation comes into play to determine if an observed frequency significantly differs from the expected frequency. If a large deviation is observed, it may cause you to question the fairness of the die or the accuracy of the model. A significantly higher or lower count of rolling a 2, such as 14 or 2 observed from 30 rolls, could be cause for investigation.