Question
This table shows the results of rolling a number cube with sides labeled 1 through 6 several times.
What is the experimental probability of rolling a 2 or a 4?
Enter your answer as a fraction in simplest form in the box.
$\text{Basic}$
$x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$
$x\frac{ }{ }$
$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
Outcome Number of times outcome occurred
1 10
2 6
3 4
4 8
5 6
6 6
What is the experimental probability of rolling a 2 or a 4?
Enter your answer as a fraction in simplest form in the box.
$\text{Basic}$
$x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$
$x\frac{ }{ }$
$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
Outcome Number of times outcome occurred
1 10
2 6
3 4
4 8
5 6
6 6
Answers
GPT-4o mini
To determine the experimental probability of rolling a 2 or a 4, we first need to find the total number of outcomes and the number of successful outcomes (rolling either a 2 or a 4).
From the table, we have:
- Number of times a 2 occurred: 6
- Number of times a 4 occurred: 8
Now, we can find the total number of successful outcomes by adding these two amounts:
\[
\text{Number of successful outcomes} = 6 + 8 = 14
\]
Next, we calculate the total number of rolls by summing the number of occurrences for all outcomes:
\[
\text{Total number of rolls} = 10 + 6 + 4 + 8 + 6 + 6 = 40
\]
The experimental probability of rolling a 2 or a 4 can be computed using the formula:
\[
P(\text{2 or 4}) = \frac{\text{Number of successful outcomes}}{\text{Total number of rolls}} = \frac{14}{40}
\]
Now, we simplify this fraction. The greatest common divisor (GCD) of 14 and 40 is 2. So we divide both the numerator and the denominator by 2:
\[
\frac{14 \div 2}{40 \div 2} = \frac{7}{20}
\]
Therefore, the experimental probability of rolling a 2 or a 4 is:
\[
\boxed{\frac{7}{20}}
\]
From the table, we have:
- Number of times a 2 occurred: 6
- Number of times a 4 occurred: 8
Now, we can find the total number of successful outcomes by adding these two amounts:
\[
\text{Number of successful outcomes} = 6 + 8 = 14
\]
Next, we calculate the total number of rolls by summing the number of occurrences for all outcomes:
\[
\text{Total number of rolls} = 10 + 6 + 4 + 8 + 6 + 6 = 40
\]
The experimental probability of rolling a 2 or a 4 can be computed using the formula:
\[
P(\text{2 or 4}) = \frac{\text{Number of successful outcomes}}{\text{Total number of rolls}} = \frac{14}{40}
\]
Now, we simplify this fraction. The greatest common divisor (GCD) of 14 and 40 is 2. So we divide both the numerator and the denominator by 2:
\[
\frac{14 \div 2}{40 \div 2} = \frac{7}{20}
\]
Therefore, the experimental probability of rolling a 2 or a 4 is:
\[
\boxed{\frac{7}{20}}
\]