SOLUTION: A bowl contains 6 red chips, 5 blue chips, and 3 white chips. If three chips are drawn, determine the probability that: a. the chips are of different colors? b. the chips ar

Algebra ->  Probability-and-statistics -> SOLUTION: A bowl contains 6 red chips, 5 blue chips, and 3 white chips. If three chips are drawn, determine the probability that: a. the chips are of different colors? b. the chips ar      Log On


   

Question 1153768: A bowl contains 6 red chips, 5 blue chips, and 3 white chips. If three
chips are drawn, determine the probability that:
a. the chips are of different colors?
b. the chips are all red?
c. two of three chips are blue?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

                       number of ways to get desired outcome
P(desired outcome) = ------------------------------------------
                     number of ways to choose 3 of the 14 chips


In every case the denominator of the fraction is

C%2814%2C3%29+=+364

a. the chips are all different colors

We need to choose 1 of the 6 red AND 1 of the 5 blue AND 1 of the 3 white:

C%286%2C1%29%2AC%285%2C1%29%2AC%283%2C1%29+=+6%2A5%2A3+=+90

P(all different colors) = 90/364

b. the chips are all red

We need to choose 3 of the 6 red AND 0 of the 5 blue AND 0 of the 3 white:

C%286%2C3%29%2AC%285%2C0%29%2AC%283%2C0%29+=+20%2A1%2A1+=+20

P(all 3 red) = 20/364

c. 2 of the 3 are blue

We need to choose 2 of the 5 blue and 1 of the 9 red or white:

C%285%2C2%29%2AC%289%2C1%29+=+10%2A9+=+90

P(2 blue) = 90/364

Simplify the fractions, or convert to decimals, if required....