Question

A box is filled with 9 red crayons, 2 blue crayons, and 5 yellow crayons. A crayon is chosen at random from the box. Find the probability that it is a red or a blue crayon. Write your answer as a fraction in simplest form.

Answer 1

`P(Red\ or\ Blue) = (11)/(16)`

Explanation:

Given

`Red = 9`

`Blue = 2`

`Yellow = 5`

Required

Probability of Red or Blue

First, it should be noted that the event described in the question are mutually exclusive or disjoint events;

Meaning that the probability of one have no effect the other;

Having said that; the Probability of Red ot Blue is as follows

`P(Red\ or\ Blue) = P(Red) + P(Blue)`

Calculating
`P(Blue)`

`P(Blue) = Number\ of\ blue\ crayon / total\ crayon`

`P(Blue) = (2)/(9+ 2 + 5)`

`P(Blue) = (2)/(16)`

Calculating
`P(Red)`

`P(Red) = Number\ of\ red\ crayon / total\ crayon`

`P(Red) = (9)/(9+ 2 + 5)`

`P(Red) = (9)/(16)`

Substitute these values in the formula given above

`P(Red\ or\ Blue) = P(Red) + P(Blue)`

`P(Red\ or\ Blue) = (9)/(16) + (2)/(16)`

Take LCM

`P(Red\ or\ Blue) = (9 + 2)/(16)`

`P(Red\ or\ Blue) = (11)/(16)`

Hence, the probability of a red or blue crayon is

`P(Red\ or\ Blue) = (11)/(16)`