18. directions select all the correct answers...
18. directions select all the correct answers. hannah and joy are playing a game. each player will take a turn spinning a spinner. the player wins if they land on a gray - section of the spinner. select two spinners in which the player is more likely to win.
Answer
# Answer:
We need to calculate the probability of landing on a gray - section for each spinner. Let's assume each section of the spinner is of equal area.
1. For the first spinner:
- Assume the spinner is divided into 8 equal - sized sections. There are 2 gray sections.
- The probability \(P_1\) of landing on a gray section is \(P_1=\frac{2}{8}=\frac{1}{4}\).
2. For the second spinner:
- Assume the spinner is divided into 6 equal - sized sections. There are 3 gray sections.
- The probability \(P_2\) of landing on a gray section is \(P_2 = \frac{3}{6}=\frac{1}{2}\).
3. For the third spinner:
- Assume the spinner is divided into 8 equal - sized sections. There are 3 gray sections.
- The probability \(P_3\) of landing on a gray section is \(P_3=\frac{3}{8}\).
4. For the fourth spinner:
- Assume the spinner is divided into 8 equal - sized sections. There are 4 gray sections.
- The probability \(P_4\) of landing on a gray section is \(P_4=\frac{4}{8}=\frac{1}{2}\).
Since \(\frac{1}{2}>\frac{3}{8}>\frac{1}{4}\), the spinners with a higher probability of winning (landing on a gray section) are the second and the fourth spinners.
# Explanation:
## Step1: Calculate probability for first spinner
\(P_1=\frac{\text{Number of gray sections}}{\text{Total number of sections}}=\frac{2}{8}=\frac{1}{4}\)
## Step2: Calculate probability for second spinner
\(P_2=\frac{\text{Number of gray sections}}{\text{Total number of sections}}=\frac{3}{6}=\frac{1}{2}\)
## Step3: Calculate probability for third spinner
\(P_3=\frac{\text{Number of gray sections}}{\text{Total number of sections}}=\frac{3}{8}\)
## Step4: Calculate probability for fourth spinner
\(P_4=\frac{\text{Number of gray sections}}{\text{Total number of sections}}=\frac{4}{8}=\frac{1}{2}\)
## Step5: Compare probabilities
We compare \(P_1=\frac{1}{4}\), \(P_2 = \frac{1}{2}\), \(P_3=\frac{3}{8}\), \(P_4=\frac{1}{2}\). Since \(\frac{1}{2}>\frac{3}{8}>\frac{1}{4}\), the second and fourth spinners have higher probabilities of winning.