Question

A plastic sack contains 20 green and yellow 14 red and yellow and 16 orange and yellow gummy

Answer 1

The probability you will randomly select a green and yellow treat is 2/25 greater than an orange and yellow treat

Step-by-step explanation:

Given

Let

`G \to Green`
`Y \to Yellow`
`R \to Red`
`O \to Orange`

`G\ n\ Y = 20`
`R\ n\ Y = 14`
`O\ n\ Y = 16`

See comment for complete question

Required

How much greater is
`P(G\ n\ Y)` than
`P(O\ n\ Y)`

First, calculate
`P(G\ n\ Y)` and
`P(O\ n\ Y)`

`P(G\ n\ Y) = (G\ n\ Y)/(Total)`

`P(O\ n\ Y) = (O\ n\ Y)/(Total)`

Where

`Total = G\ n\ Y + R\ n\ Y + O\ n\ Y`

`Total = 20 + 14 + 16`

`Total =50`

So:

`P(G\ n\ Y) = (G\ n\ Y)/(Total)`

`P(G\ n\ Y) = (20)/(50)`

`P(G\ n\ Y) = (2)/(5)`

`P(O\ n\ Y) = (O\ n\ Y)/(Total)`

`P(O\ n\ Y) = (16)/(50)`

`P(O\ n\ Y) = (8)/(25)`

Calculate the difference (d) between both

`d = P(G\ n\ Y) - P(O\ n\ Y)`

`d = (2)/(5) - (8)/(25)`

Take LCM

`d = (10-8)/(25)`

`d = (2)/(25)`