Question

maya wants to perform an experiment with a spinner labeled a, b, and c. the theoretical probabilities for each section are: p(a) = 1/2, p(b) = 1/4, and p(c) = 1/4. which spinner could she use?

Explanation:

Step1: Recall probability formula

Probability of an event = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Analyze first spinner

It has 4 equal - sized sections. If we consider it, $P(A)=\frac{1}{4}$, $P(B)=\frac{1}{4}$, $P(C)=\frac{1}{4}$, which does not match the given probabilities.

Step3: Analyze second spinner

It has 8 equal - sized sections. There are 4 sections labeled A, 2 sections labeled B and 2 sections labeled C. So $P(A)=\frac{4}{8}=\frac{1}{2}$, $P(B)=\frac{2}{8}=\frac{1}{4}$, $P(C)=\frac{2}{8}=\frac{1}{4}$, which matches the given probabilities.

Step4: Analyze third spinner

It has 4 equal - sized sections. $P(A)=\frac{1}{4}$, $P(B)=\frac{1}{4}$, $P(C)=\frac{2}{4}=\frac{1}{2}$, which does not match the given probabilities.

Step5: Analyze fourth spinner

It has 8 equal - sized sections. $P(A)=\frac{2}{8}=\frac{1}{4}$, $P(B)=\frac{4}{8}=\frac{1}{2}$, $P(C)=\frac{2}{8}=\frac{1}{4}$, which does not match the given probabilities.

Answer:

The second spinner.