Question

prisha rolls a fair number cube multiple times and records the result of each roll. her results are shown in the table.
number cube
number\tobserved frequency
1\t18
2\t16
3\t24
4\t26
5\t16
6\t20
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.
mark this and return.

Explanation:

Step1: Calculate total trials

Sum all observed frequencies: \(18 + 16 + 24 + 26 + 16 + 20 = 120\)

Step2: Find experimental probability of 3

Experimental probability \(= \frac{\text{Frequency of 3}}{\text{Total trials}} = \frac{24}{120} = \frac{1}{5}\)

Step3: Find theoretical probability of 3

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

Step4: Find the difference

\(\frac{1}{5} - \frac{1}{6} = \frac{6 - 5}{30} = \frac{1}{30}\)

Answer:

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