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Kevin has a spinner with 10 equal sections, 2 sections each of red, blue, green, yellow, and purple. Kevin spins the spinner 180 times. Kevin determines how many times the spinner will land on red or green, and his work is shown below.

[tex]\[
\begin{aligned}
P(\text{red or green}) & = \frac{\text{Number of red or green sections}}{\text{Total number of sections}} \cdot \text{Number of spins} \\
& = \frac{4}{10} \cdot 180 \\
& = 72
\end{aligned}
\][/tex]

What mistake did Kevin make, if any?

A. Kevin has the formula reversed; it should be the total number of sections over the number of red or green sections.

B. Kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections.

C. Kevin should multiply by the number of sections in the spinner rather than the total number of spins.

D. Kevin calculated the prediction correctly and did not make any mistakes.



Answer :

GinnyAnswer
Kevin's mistake lies in the numerator of his fraction for the probability. He only accounted for either the red or the green sections separately.

Here's the correct step-by-step solution:

1. Identify the total number of sections:
The spinner has 10 equal sections.

2. Identify the number of sections that are either red or green:
There are 2 red sections and 2 green sections, which makes a total of 4 sections (2 red + 2 green).

3. Set up the probability:
To find the probability of landing on red or green, you use the ratio of the favorable outcomes (red or green sections) to the total outcomes (all sections).

[tex]\[ P(\text{red or green}) = \frac{\text{Number of red or green sections}}{\text{Total number of sections}} = \frac{4}{10} \][/tex]

4. Calculate the expected number of times the spinner lands on red or green out of 180 spins:
Multiply the probability by the total number of spins:

[tex]\[ \frac{4}{10} \times 180 = 0.4 \times 180 = 72 \][/tex]

So, Kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections.

The correct prediction for the number of times the spinner will land on red or green is [tex]\( 72 \)[/tex].

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