Question

A box contains 4 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors

Answer 1

`(4C1 \cdot 2C1)/(6C2) =(8)/(15)`

Explanation:

A box contains 4 red chips and 2 blue chips

total 4+2= 6 chips

the chips are different colors. we need to select 1 chip from red and 1 chip from blue

we can select 1 red chip from 4 red chips in 4C1 ways

`4C1=(4!)/(1!(4-1)!) =4`

we can select 1 blue chip from 2 blue chips in 2C1 ways

`2C1=(2!)/(1!(2-1)!) =2`

select 2 chips from 6 chips in 6C2 ways

`6C2=(6!)/(2!(6-2)!) =15`

probability that the chips are different colors

`(4C1 \cdot 2C1)/(6C2) =(8)/(15)`