Question

luis rolled a number cube 60 times. he rolled the number 6 four times. which is most likely the cause of the discrepancy between luiss experimental outcome and the predicted outcome?
he performed too many trials.
he did not perform enough trials.
he needs to add the number 6 to the number of times it occurred.
he needs to subtract the experimental outcome from the predicted outcome.

Explanation:

Step1: Calculate theoretical probability

The theoretical probability of rolling a 6 on a fair number cube is \( P(6)=\frac{1}{6} \).

Step2: Calculate expected number of 6s

If the cube is rolled \( n = 60 \) times, the expected (theoretical) number of 6s is \( E=60\times\frac{1}{6}=10 \).

Step3: Analyze the number of trials

Since \( 60 \) is not a very large number of trials (in probability, as the number of trials \( n\) approaches infinity, the experimental probability approaches the theoretical probability more closely), a relatively small \( n = 60 \) can lead to a discrepancy between experimental (he rolled 6 four - times) and theoretical results.

Answer:

He did not perform enough trials.