Question

A deli has 6 packs of cheese, out of those are 2 that are spoiled. Three packs of cheese are randomly sampled.

a) What is the probability that there will be no spoiled cheese packs in the sample of 3.

b) What is the probability that out of the 3 cheese packets that are sampled, there is one pack of spoiled cheese?

Answer 1

Total packs 6

Total spoilt 2 , total good = 4

Way to select 3 packs from 6 packs  ⁶C₃ = 20

Ways to select 3 good packet from 4 good is ⁴C_{3 =} 4

_{a) probability of choosing no spoilt packs from sample of 3 is}

_{4/20 = 1/5}

b) ways to select 2 good packet from 4 good packet is

⁴C₂ = 6 ways

Ways to select 1 spoilt from 2 spoilt is 2 ways only

So required probability that out of 3 sample , 2, are good and one is spoilt is

(6*2)/20 = 12/20 = 3/5 is the required probability.