Question

the spinner below is divided into 8 congruent sections. select three statements that are true about the spinner. spinning a 1 is more likely than spinning any other number. the sample space of the spinner is {1, 1, 1, 2, 3, 3, 4, 4}. you are equally likely to spin a 3 as spin a 4. you are equally likely to spin an even or odd number. you are 3 times more likely to spin a 3 than a 1. you are more likely to spin a 2 than a 3.

Explanation:

First, let's analyze the number of each number on the spinner:

• Number of 1s: 3
• Number of 2s: 1
• Number of 3s: 2
• Number of 4s: 2

Step 1: Analyze "Spinning a 1 is more likely than spinning any other number"

The probability of spinning a 1 is $\frac{3}{8}$. The probability of spinning a 2 is $\frac{1}{8}$, a 3 is $\frac{2}{8}$, and a 4 is $\frac{2}{8}$. Since $\frac{3}{8} > \frac{2}{8} > \frac{1}{8}$, spinning a 1 is more likely than any other number. So this statement is true.

Step 2: Analyze "The sample space of the spinner is {1, 1, 1, 2, 3, 3, 4, 4}"

The sample space should list all possible outcomes. Since there are 3 sections with 1, 1 section with 2, 2 sections with 3, and 2 sections with 4, the sample space is indeed {1, 1, 1, 2, 3, 3, 4, 4}. So this statement is true.

Step 3: Analyze "You are equally likely to spin a 3 as spin a 4"

The number of 3s is 2 and the number of 4s is 2. So the probability of spinning a 3 is $\frac{2}{8}$ and the probability of spinning a 4 is $\frac{2}{8}$. Thus, they are equally likely. This statement is true.

Step 4: Analyze "You are equally likely to spin an even or odd number"

Number of odd numbers (1, 3): 3 + 2 = 5. Number of even numbers (2, 4): 1 + 2 = 3. Probability of odd: $\frac{5}{8}$, probability of even: $\frac{3}{8}$. Not equal. So this statement is false.

Step 5: Analyze "You are 3 times more likely to spin a 3 than a 1"

Probability of 3: $\frac{2}{8}$, probability of 1: $\frac{3}{8}$. $\frac{2}{8}$ is not 3 times $\frac{3}{8}$. So this statement is false.

Step 6: Analyze "You are more likely to spin a 2 than a 3"

Probability of 2: $\frac{1}{8}$, probability of 3: $\frac{2}{8}$. $\frac{1}{8} < \frac{2}{8}$, so less likely. This statement is false.

Answer:

• Spinning a 1 is more likely than spinning any other number.
• The sample space of the spinner is {1, 1, 1, 2, 3, 3, 4, 4}.
• You are equally likely to spin a 3 as spin a 4.