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