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Maya wants to perform an experiment with a spinner labeled [tex]$A$[/tex], [tex]$B$[/tex], and [tex]$C$[/tex]. The theoretical probabilities for each section are: [tex]$P(A)=\frac{1}{2}$[/tex], [tex]$P(B)=\frac{1}{4}$[/tex], and [tex]$P(C)=\frac{1}{4}$[/tex]. Which spinner could she use?

Sagot :

GinnyAnswer
To determine which spinner Maya could use, we need to ensure that the spinner reflects the theoretical probabilities of landing on sections labeled [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex]. Specifically, we want a spinner that divides the circle into three sections with these exact probabilities:

- Probability for section [tex]\( A \)[/tex]: [tex]\( P(A) = \frac{1}{2} = 0.5 \)[/tex]
- Probability for section [tex]\( B \)[/tex]: [tex]\( P(B) = \frac{1}{4} = 0.25 \)[/tex]
- Probability for section [tex]\( C \)[/tex]: [tex]\( P(C) = \frac{1}{4} = 0.25 \)[/tex]

Based on these probabilities, we can make the following observations:

1. Section [tex]\( A \)[/tex] should occupy half of the spinner (50% of the total area).
- This means if we imagine dividing the spinner into 2 equal parts, section [tex]\( A \)[/tex] would take up one of those parts.

2. Section [tex]\( B \)[/tex] and Section [tex]\( C \)[/tex] should each occupy one-fourth of the spinner (25% each of the total area).
- This implies that if we further divide the remaining half of the spinner (not occupied by [tex]\( A \)[/tex]) into 2 equal parts, section [tex]\( B \)[/tex] would take up one part and section [tex]\( C \)[/tex] the other.

Visually, the spinner would look as follows:
- Start by drawing a circle.
- Divide the circle into two equal halves. One half represents [tex]\( A \)[/tex] (which corresponds to 50% of the area).
- Take the remaining half and divide it into two equal quarters. One quarter represents [tex]\( B \)[/tex] (25%), and the other quarter represents [tex]\( C \)[/tex] (25%).

Through this setup, we have ensured that:
- Section [tex]\( A \)[/tex] occupies 50% of the circle,
- Section [tex]\( B \)[/tex] occupies 25% of the circle, and
- Section [tex]\( C \)[/tex] occupies 25% of the circle.

So, the spinner Maya should use is one that divides the circle into three sections with the following proportions:
- 50% for section [tex]\( A \)[/tex]
- 25% for section [tex]\( B \)[/tex]
- 25% for section [tex]\( C \)[/tex]

This configuration reflects the theoretical probabilities perfectly.
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