Question

a spinner from 1-6 (1 is blue) (2 is purple) (3 is red) (4 is yellow) (5 is yellow) (6 is red)
what the theoretical probability of spinning a 1
what the theoretical probability of spinning an odd number
what the theoretical probability of spinning a 9
what the theoretical probability of spinning red

Answer 1

To compute the theoretical probabilities, we first need to understand the total number of outcomes when spinning the spinner and how many of those outcomes correspond to the events in question.

The outcomes of the spinner are:
1 (blue)
2 (purple)
3 (red)
4 (yellow)
5 (yellow)
6 (red)

This gives us a total of 6 outcomes.

### Theoretical Probability of Spinning a 1
The event of spinning a 1 occurs only once (only one blue sector).
- Number of favorable outcomes: 1
- Probability = Number of favorable outcomes / Total outcomes = 1/6

**Probability of spinning a 1:** \(\frac{1}{6}\)

### Theoretical Probability of Spinning an Odd Number
The odd numbers on the spinner are 1, 3, and 5.
- Number of favorable outcomes: 3 (1, 3, and 5)
- Probability = 3/6 = 1/2

**Probability of spinning an odd number:** \(\frac{1}{2}\)

### Theoretical Probability of Spinning a 9
There is no outcome of 9 on the spinner (the highest number is 6).
- Number of favorable outcomes: 0
- Probability = 0/6 = 0

**Probability of spinning a 9:** \(0\)

### Theoretical Probability of Spinning Red
The red sectors on the spinner are represented by the numbers 3 and 6.
- Number of favorable outcomes: 2 (3 and 6)
- Probability = 2/6 = 1/3

**Probability of spinning red:** \(\frac{1}{3}\)

### Summary of Probabilities
- Probability of spinning a 1: \(\frac{1}{6}\)
- Probability of spinning an odd number: \(\frac{1}{2}\)
- Probability of spinning a 9: \(0\)
- Probability of spinning red: \(\frac{1}{3}\)