Question

a number cube was rolled as part of an experiment. the results are shown in the table. explain how to find the experimental probability of rolling a 6.

number	frequency
2	11
3	9
4	8
5	10
6	9

Explanation:

Answer:

To find the experimental probability of rolling a 6, follow these steps:

Step 1: Find the total number of trials

First, sum up all the frequencies. The frequencies are 13 (for 1), 11 (for 2), 9 (for 3), 8 (for 4), 10 (for 5), and 9 (for 6).

$$ \text{Total trials} = 13 + 11 + 9 + 8 + 10 + 9 $$

$$ \text{Total trials} = 13 + 11 = 24; \quad 24 + 9 = 33; \quad 33 + 8 = 41; \quad 41 + 10 = 51; \quad 51 + 9 = 60 $$

So, the total number of trials is 60.

Step 2: Identify the frequency of rolling a 6

From the table, the frequency of rolling a 6 is 9.

Step 3: Calculate the experimental probability

The formula for experimental probability is:

$$ \text{Experimental Probability} = \frac{\text{Number of successful trials}}{\text{Total number of trials}} $$

For rolling a 6, the number of successful trials is 9 (frequency of 6), and the total number of trials is 60.

$$ \text{Experimental Probability of rolling a 6} = \frac{9}{60} $$

Simplify the fraction:

$$ \frac{9}{60} = \frac{3}{20} = 0.15 $$

So, the experimental probability of rolling a 6 is \(\frac{3}{20}\) or 0.15.