Let's analyze Kevin's method step-by-step to identify any mistakes he may have made.
1. Identify the total number of sections on the spinner:
Kevin has 10 equal sections on the spinner.
2. Identify the number of sections that are red or green:
There are 2 red sections and 2 green sections.
Therefore, the total number of sections that are either red or green is:
[tex]\( 2 + 2 = 4 \)[/tex]
3. Determine the probability of landing on a red or green section:
The probability is given by the ratio of the number of red or green sections to the total number of sections:
[tex]\[
\text{Probability of red or green} = \frac{\text{Number of red or green sections}}{\text{Total number of sections}} = \frac{4}{10} = 0.4
\][/tex]
4. Calculate the expected number of times the spinner will land on red or green in 180 spins:
Multiply the probability by the number of spins:
[tex]\[
\text{Expected spins on red or green} = \text{Probability} \times \text{Number of spins} = 0.4 \times 180 = 72
\][/tex]
5. Analyze Kevin's calculation:
Kevin’s calculation can be broken down into the following steps:
[tex]\[
P(\text{red or green}) = \frac{\text{Number of red sections}}{\text{Total number of sections}} \cdot 2 \times \text{Number of spins}
\][/tex]
However, Kevin appears to have used:
[tex]\[
P(\text{red or green}) = \frac{2}{10}(180)
\][/tex]
and arrived at 36.
The mistake Kevin made is that he used only the number of red sections (2) in his calculation instead of using the total number of red or green sections (4). Therefore, the correct calculation should use 4 in the numerator:
To summarize:
- Kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections.
Therefore, the correct answer is:
Kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections.
