A​ 12-sided solid has faces numbered 1 to 12. The table shows the results of rolling the solid 200 times. Find the experimental probability of rolling a number greater than 10.

Question

Results
Number rolled
1
2
3
4
5
6
7
8
9
10
11
12
Total
Frequency
20
12
15
15
23
14
16
24
18
11
16
16
200
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Part 1
The experimental probability of rolling a number greater than 10 is
  
enter your response here.
​(Simplify your​ answer.)

Answer 1

To find the experimental probability of rolling a number greater than 10, we first need to determine the number of times a number greater than 10 (which includes only 11 and 12) was rolled.

From the provided frequency table:

• The frequency of rolling a 11 is 16.
• The frequency of rolling a 12 is 16.

Now, we add these frequencies together to get the total frequency of rolling a number greater than 10: \[ \text{Frequency of rolling a number greater than 10} = 16 + 16 = 32 \]

Next, we calculate the experimental probability using the formula: \[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total outcomes}} = \frac{32}{200} \]

Now, we can simplify this fraction: \[ \frac{32}{200} = \frac{32 \div 8}{200 \div 8} = \frac{4}{25} \]

Thus, the experimental probability of rolling a number greater than 10 is: \[ \boxed{\frac{4}{25}} \]