Questions: 2. At a fair, each person can spin two wheels of chance. The first wheel has the numbers 1,2 , and 3 . The second wheel has the letters A and B. (a) List all the possible outcomes of the compound event. (b) If you spin both wheels, what is the probability that you get either a 1 or an A? Explain.

2. At a fair, each person can spin two wheels of chance. The first wheel has the numbers 1,2 , and 3 . The second wheel has the letters A and B.
(a) List all the possible outcomes of the compound event.
(b) If you spin both wheels, what is the probability that you get either a 1 or an A? Explain.

Transcript text: 2. At a fair, each person can spin two wheels of chance. The first wheel has the numbers 1,2 , and 3 . The second wheel has the letters A and B. (a) List all the possible outcomes of the compound event. (b) If you spin both wheels, what is the probability that you get either a 1 or an A? Explain.

Solution

Solution Steps

Step 1: List all possible outcomes of the compound event

The first wheel has the numbers \( \{1, 2, 3\} \), and the second wheel has the letters \( \{A, B\} \). To list all possible outcomes, pair each number with each letter. The possible outcomes are: \[ (1, A), (1, B), (2, A), (2, B), (3, A), (3, B) \] The total number of possible outcomes is \( 3 \times 2 = 6 \).

Step 2: Identify favorable outcomes for getting either a 1 or an A

To find the probability of getting either a 1 or an A, identify the favorable outcomes:

Outcomes with 1: \( (1, A), (1, B) \)
Outcomes with A: \( (1, A), (2, A), (3, A) \)

Note that \( (1, A) \) is counted twice, so the total number of unique favorable outcomes is \( 4 \).

Step 3: Calculate the probability

The probability \( P \) of getting either a 1 or an A is the ratio of the number of favorable outcomes to the total number of possible outcomes: \[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{6} = \frac{2}{3} \]