Question
A number cube with faces numbered from 1 to 6 will be rolled 15 times.(1 point)
Determine how many outcomes are less than 5 on the number cube.
outcomes
Question 2
Theoretically, how many of the 15 rolls should result in a number less than 5?
Complete the proportion.
(2 points)
Drop target 1
Drop target 2
Question 3
Theoretically, how many of the 15 rolls should result in a number less than 5?(1 point)
Responses
2.5
2.5
5
5
10
10
12.5
Determine how many outcomes are less than 5 on the number cube.
outcomes
Question 2
Theoretically, how many of the 15 rolls should result in a number less than 5?
Complete the proportion.
(2 points)
Drop target 1
Drop target 2
Question 3
Theoretically, how many of the 15 rolls should result in a number less than 5?(1 point)
Responses
2.5
2.5
5
5
10
10
12.5
Answers
GPT-4o mini
To solve these questions, let's break it down step by step.
**Question 1: Determine how many outcomes are less than 5 on the number cube.**
The faces of a number cube (die) are numbered from 1 to 6. The numbers that are less than 5 are 1, 2, 3, and 4.
So there are **4 outcomes** that are less than 5 on the number cube.
**Question 2: Theoretically, how many of the 15 rolls should result in a number less than 5?**
To find this, we need to look at the total outcomes. There are 4 favorable outcomes (1, 2, 3, and 4) out of a total of 6 possible outcomes (1, 2, 3, 4, 5, 6).
The proportion of outcomes that are less than 5 is:
\[
\text{Proportion} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{4}{6} = \frac{2}{3}
\]
Now, if we roll the die 15 times, we can calculate the expected number of times a number less than 5 would appear by multiplying this proportion by 15:
\[
\text{Expected outcomes} = \frac{2}{3} \times 15 = 10
\]
**Complete the proportion:**
- Drop target 1: \(\frac{4}{6}\) (this is the proportion of favorable outcomes)
- Drop target 2: \(\frac{10}{15}\) (this is the expected outcomes for 15 rolls based on the proportion)
**Question 3: Theoretically, how many of the 15 rolls should result in a number less than 5?**
From the calculations above, the answer is:
**10**
So the answers to the questions are:
1. **4 outcomes**
2. Proportion: \(\frac{4}{6}\) for favorable outcomes and \(\frac{10}{15}\) for expected outcomes.
3. Theoretical outcome: **10**.
**Question 1: Determine how many outcomes are less than 5 on the number cube.**
The faces of a number cube (die) are numbered from 1 to 6. The numbers that are less than 5 are 1, 2, 3, and 4.
So there are **4 outcomes** that are less than 5 on the number cube.
**Question 2: Theoretically, how many of the 15 rolls should result in a number less than 5?**
To find this, we need to look at the total outcomes. There are 4 favorable outcomes (1, 2, 3, and 4) out of a total of 6 possible outcomes (1, 2, 3, 4, 5, 6).
The proportion of outcomes that are less than 5 is:
\[
\text{Proportion} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{4}{6} = \frac{2}{3}
\]
Now, if we roll the die 15 times, we can calculate the expected number of times a number less than 5 would appear by multiplying this proportion by 15:
\[
\text{Expected outcomes} = \frac{2}{3} \times 15 = 10
\]
**Complete the proportion:**
- Drop target 1: \(\frac{4}{6}\) (this is the proportion of favorable outcomes)
- Drop target 2: \(\frac{10}{15}\) (this is the expected outcomes for 15 rolls based on the proportion)
**Question 3: Theoretically, how many of the 15 rolls should result in a number less than 5?**
From the calculations above, the answer is:
**10**
So the answers to the questions are:
1. **4 outcomes**
2. Proportion: \(\frac{4}{6}\) for favorable outcomes and \(\frac{10}{15}\) for expected outcomes.
3. Theoretical outcome: **10**.