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

5

10

12.5

Answer 1

Let's address each question step by step:

### Question 1:
Outcomes that are less than 5 on a number cube (with faces numbered from 1 to 6) would be the numbers 1, 2, 3, and 4. There are 4 outcomes that are less than 5.

So, the answer to Question 1 is:
**4 outcomes**

### Question 2:
To determine how many of the 15 rolls should result in a number less than 5, we start by calculating the probability of rolling a number less than 5. The faces of the cube that are less than 5 are 1, 2, 3, and 4, which gives us 4 favorable outcomes.

The total number of faces on the cube is 6, so the probability \( P \) of rolling a number less than 5 is:
\[
P(\text{less than 5}) = \frac{\text{Number of outcomes less than 5}}{\text{Total outcomes}} = \frac{4}{6} = \frac{2}{3}
\]

Now, using this probability, let's set up the proportion for the number of rolls out of 15 that should result in a number less than 5:

\[\frac{\text{Rolls less than 5}}{15} = \frac{2}{3}\]

To find the number of rolls less than 5, we can cross-multiply:
\[
\text{Rolls less than 5} = 15 \cdot \frac{2}{3} = 10
\]

So for Part 2, you would fill in:
**Drop target 1:** Rolls less than 5
**Drop target 2:** 10

### Question 3:
From our calculation in Question 2, we found that theoretically, you should expect **10 rolls** out of the 15 to result in a number less than 5.

So, the answer to Question 3 is:
**10**