Answer:
The probability you will randomly select a green and yellow treat is 2/25 greater than an orange and yellow treat
Explanation:
Given
Let
[tex]G \to Green[/tex] [tex]Y \to Yellow[/tex] [tex]R \to Red[/tex] [tex]O \to Orange[/tex]
[tex]G\ n\ Y = 20[/tex] [tex]R\ n\ Y = 14[/tex] [tex]O\ n\ Y = 16[/tex]
See comment for complete question
Required
How much greater is [tex]P(G\ n\ Y)[/tex] than [tex]P(O\ n\ Y)[/tex]
First, calculate [tex]P(G\ n\ Y)[/tex] and [tex]P(O\ n\ Y)[/tex]
[tex]P(G\ n\ Y) = \frac{G\ n\ Y}{Total}[/tex]
[tex]P(O\ n\ Y) = \frac{O\ n\ Y}{Total}[/tex]
Where
[tex]Total = G\ n\ Y + R\ n\ Y + O\ n\ Y[/tex]
[tex]Total = 20 + 14 + 16[/tex]
[tex]Total =50[/tex]
So:
[tex]P(G\ n\ Y) = \frac{G\ n\ Y}{Total}[/tex]
[tex]P(G\ n\ Y) = \frac{20}{50}[/tex]
[tex]P(G\ n\ Y) = \frac{2}{5}[/tex]
[tex]P(O\ n\ Y) = \frac{O\ n\ Y}{Total}[/tex]
[tex]P(O\ n\ Y) = \frac{16}{50}[/tex]
[tex]P(O\ n\ Y) = \frac{8}{25}[/tex]
Calculate the difference (d) between both
[tex]d = P(G\ n\ Y) - P(O\ n\ Y)[/tex]
[tex]d = \frac{2}{5} - \frac{8}{25}[/tex]
Take LCM
[tex]d = \frac{10-8}{25}[/tex]
[tex]d = \frac{2}{25}[/tex]
