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.