Sure, let's tackle this problem step-by-step.
### (a) List all the possible outcomes of the compound event.
To find all possible outcomes, we need to consider each number on the first wheel and pair it with each letter on the second wheel. The outcomes can be represented as ordered pairs (number, letter).
Here are the steps to list all possible outcomes:
1. Pair the number 1 with each letter:
- (1, A)
- (1, B)
2. Pair the number 2 with each letter:
- (2, A)
- (2, B)
3. Pair the number 3 with each letter:
- (3, A)
- (3, B)
Thus, the complete list of all possible outcomes is:
- (1, A)
- (1, B)
- (2, A)
- (2, B)
- (3, A)
- (3, B)
So, there are a total of 6 possible outcomes.
### (b) If you spin both wheels, what is the probability that you get either a 1 or an A? Explain.
First, we need to establish the total number of possible outcomes, which we've already determined to be 6.
Next, we'll identify the number of favorable outcomes where we get either a 1 or an A. We'll list all outcomes where either condition is met:
1. Outcomes that include the number 1:
- (1, A)
- (1, B)
2. Outcomes that include the letter A:
- (1, A)
- (2, A)
- (3, A)
Combining these lists and eliminating any duplicates, the unique favorable outcomes are:
- (1, A)
- (1, B)
- (2, A)
- (3, A)
Thus, there are 4 favorable outcomes.
The formula for probability is given by:
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \][/tex]
Using the numbers we've identified:
[tex]\[ \text{Probability} = \frac{4}{6} = \frac{2}{3} \][/tex]
So, the probability that you get either a 1 or an A is [tex]\(\frac{2}{3}\)[/tex], which is approximately 0.6667 or 66.67%.
