A spinner with 9 equal sections labeled with the letters A, A, B, B, B, C, C, C, and D is spun 198 times. Which of the following correctly predicts how many times the spinner will land on the letter B?(1 point)

Responses

22 times
22 times

66 times
66 times

198 times
198 times

44 times

1 answer

To determine how many times the spinner will land on the letter B, we need to calculate the probability of landing on B based on the spinner's sections.

The spinner is divided into 9 equal sections:

  • A: 2 sections
  • B: 3 sections
  • C: 3 sections
  • D: 1 section

The total sections add up to 9.

The probability of landing on B in a single spin is:

\[ P(B) = \frac{\text{Number of B sections}}{\text{Total sections}} = \frac{3}{9} = \frac{1}{3} \]

If the spinner is spun 198 times, we can predict the number of times it will land on B by multiplying the total spins by the probability:

\[ \text{Expected number of B} = 198 \times P(B) = 198 \times \frac{1}{3} = 66 \]

Thus, the spinner will land on the letter B approximately 66 times.

The correct response is: 66 times.