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
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 1/30 greater than the theoretical probability of rolling a 3.

the experimental probability of rolling a 3 is 1/30 less than the theoretical probability of rolling a 3.

Explanation:

Step1: Calculate total number of rolls

$18 + 16+24 + 26+16+20=120$

Step2: Calculate experimental probability of rolling a 3

The observed frequency of rolling a 3 is 24. Experimental probability $P_{exp}=\frac{24}{120}=\frac{1}{5}$

Step3: Calculate theoretical probability of rolling a 3

For a fair number - cube, there are 6 possible outcomes. Theoretical probability $P_{theo}=\frac{1}{6}$

Step4: Find the difference

$P_{exp}-P_{theo}=\frac{1}{5}-\frac{1}{6}=\frac{6 - 5}{30}=\frac{1}{30}$

Answer:

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