Question 1

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
12.5
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1 answer

Let’s answer the questions step by step.

Question 1: To determine how many outcomes are less than 5 on a number cube (which has faces numbered from 1 to 6), we consider the following outcomes:

  • 1
  • 2
  • 3
  • 4

There are 4 outcomes (1, 2, 3, 4) that are less than 5.

Answer: 4 outcomes.


Question 2: To find the theoretical number of rolls resulting in a number less than 5 from 15 rolls, we can first establish the probability of rolling a number less than 5.

The total outcomes on a number cube = 6
The favorable outcomes (less than 5) = 4

So, the probability \( P \) of rolling a number less than 5 is: \[ P = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{4}{6} = \frac{2}{3} \]

Using this probability, we can set up a proportion based on the total number of rolls:

  • If 6 rolls result in a number less than 5, how many would result in that out of 15 rolls?

This gives us the proportion: \[ \frac{4}{6} = \frac{x}{15} \]

Solving for \( x \): \[ x = 15 \times \frac{4}{6} = 15 \times \frac{2}{3} = 10 \]

Thus, theoretically, 10 of the 15 rolls should result in a number less than 5.

Answer for Question 2: In terms of completion, you would say:

  • Drop target 1: 4
  • Drop target 2: 6

Question 3: To directly answer how many of the 15 rolls should result in a number less than 5, we have already calculated this in Question 2.

So, the theoretical number of rolls resulting in a number less than 5 from 15 rolls is:

Answer: 10.