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].
