Question

number cube
observed frequency
1 18
2 16
3 24
4 26
5 16
6 20
how does the experimental probability of rolling a 3 compare with the theoretical probability of rolling a 3?
the experimental probability of rolling a 3 is (\frac{1}{30}) greater than the theoretical probability of rolling a 3.
the experimental probability of rolling a 3 is (\frac{1}{30}) less than the theoretical probability of rolling a 3.
the experimental probability of rolling a 3 is (\frac{2}{3}) greater than the theoretical probability of rolling a 3.

Explanation:

Step1: Calculate total trials

Sum the frequencies: \(18 + 16 + 24 + 26 + 16 + 20 = 120\).

Step2: Find experimental probability of 3

Frequency of 3 is 24, so experimental probability \(= \frac{24}{120} = \frac{1}{5}\).

Step3: Find theoretical probability of 3

A cube has 6 sides, so theoretical probability \(= \frac{1}{6}\).

Step4: Compare the two probabilities

Find the difference: \(\frac{1}{5} - \frac{1}{6} = \frac{6 - 5}{30} = \frac{1}{30}\). So experimental probability is \(\frac{1}{30}\) greater than theoretical.

Answer:

The experimental probability of rolling a 3 is \(\frac{1}{30}\) greater than the theoretical probability of rolling a 3 (the option stating this).