Maya wants to perform an experiment with a spinner labeled A, B, and C. The theoretical probabilities for each section are: P(A) = ½, P(B) = ¼, and P(C) = ¼. Which spinner could she use?

Question

A spinner divided into 4 equal sections labeled A, B, C, D.
A spinner divided into 8 equal sections labeled A, A, A, A, B, B, C, C.
A spinner divided into 4 equal sections labeled A, B, C, C.
A spinner divided into 8 equal sections labeled A, A, B, B, B, C, C, C.

Answer 1

To determine which spinner corresponds to the theoretical probabilities provided (P(A) = ½, P(B) = ¼, P(C) = ¼), we need to evaluate each option in terms of the proportions of A, B, and C on the spinners.

1. Spinner divided into 4 equal sections labeled A, B, C, D:

   • A: 1 section
   • B: 1 section
   • C: 1 section
   • D: 1 section
   • P(A) = 1/4, P(B) = 1/4, P(C) = 1/4 (D = unused section)
   • This is not suitable since P(A) = ½ is not satisfied.

2. Spinner divided into 8 equal sections labeled A, A, A, A, B, B, C, C:

   • A: 4 sections
   • B: 2 sections
   • C: 2 sections
   • P(A) = 4/8 = 1/2, P(B) = 2/8 = 1/4, P(C) = 2/8 = 1/4
   • This is suitable as it matches the theoretical probabilities.

3. Spinner divided into 4 equal sections labeled A, B, C, C:

   • A: 1 section
   • B: 1 section
   • C: 2 sections
   • P(A) = 1/4, P(B) = 1/4, P(C) = 2/4 = 1/2
   • This is not suitable since P(A) = ½ is not satisfied.

4. Spinner divided into 8 equal sections labeled A, A, B, B, B, C, C, C:

   • A: 2 sections
   • B: 3 sections
   • C: 3 sections
   • P(A) = 2/8 = 1/4, P(B) = 3/8, P(C) = 3/8
   • This does not match the probabilities.

Thus, the spinner that Maya could use is the second option: A spinner divided into 8 equal sections labeled A, A, A, A, B, B, C, C.