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	observed frequency
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... less than the theoretical probability of rolling a 3.

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Explanation:

Step1: Calculate total rolls

Add all observed frequencies:
$18 + 16 + 24 + 26 + 16 + 20 = 120$

Step2: Find experimental probability

Divide frequency of 3 by total rolls:
$\text{Experimental Probability} = \frac{24}{120} = \frac{1}{5}$

Step3: Identify theoretical probability

For a fair cube, $P(3) = \frac{1}{6}$

Step4: Compute the difference

Subtract theoretical from experimental:
$\frac{1}{5} - \frac{1}{6} = \frac{6 - 5}{30} = \frac{1}{30}$

Answer:

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