Question

A candy dish contains 6 blue candies and 5 red candies. A child reaches up and picks 3 candies without looking.

a) What is the probability that the child gets 3 blue candies?
b) What is the probability the child gets at least one candy of each colour?

Answer 1

We have 6 Blue candies

And 5 Red candies

Total = 11 candies

A child picks 3 candies.

a) P(3 Blue candies)

= ways to pick 3 blue / ways to pick 3 candies = = 20/165 = 0.12

b) P(One candy of each color)

There are two cases:

• Case 1: 2 blue + 1 red

P(2 blue + 1 red) = = 75/165

• Case 2: 1 blue + 2 red

P( blue + 2 red) = = 60/165

P(One candy of each color) = P(2 blue + 1 red) + P( blue + 2 red)

=> (75+60)/165 = 135/165 = 0.818