18. directions select all the correct answers. hannah and joy are playing a game. each player will take a…

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.

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.