Question

Two faces of a six-sided die are painted red, two are painted brown, and two are painted green. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded. (a) What is the probability that the three rolls produce exactly two different colors? (b) What is the probability that the three rolls produce at least one red?

Answer 1

a)

P(three rolls produce two different colors)=P(choose a color from 3 which appear twice and then choose a color which appear once and then arrange them in 3 places)=³C₂*²C₁*³C₂/3³ =3*2*3/27=18/27=2/3

b)

P(at least one roll is red)=1-P(all three rolls are non red) =1-(2/3)³ =19/27