Question

A box contains one red, two white and two orange marbles. Two marbles are drawn at random without replacement.

a) What is the probability that both are the same color?

b) What is the probability that they are different colors?

c) What is the probability that neither is red?

Answer 1

The total number of ways ro select 2 marbles from 5 marbles are ⁵C₂ = 10

a) Both are the same colors , means we cannot consider Red marble

The Mutually exclusive ways are both are either white or orange

b) They are of different colors, the mutually exclusive combinations are RW, RO, WO

c) Neither is Red

For the event at least one is red , the mutually exclusive combinations are RW,RO

P(At least One is Red) = ( 1 *2 +1 *2)/10 = 4/10 = 0.4

P(Neither is Red) = 1- P(At least one is red) = 1-0.4 = 0.6