Roses are shipped in packages of 9 roses, each containing 3 red roses and 6 whit

Question

Roses are shipped in packages of 9 roses, each containing 3 red roses and 6 white roses. A florist asks
his color-blind assistant (who cannot tell the difference between red and white roses) to arrange two
such packages into 3 bouquets, each containing 6 roses. Since the assistant cannot distinguish red
from white, assume that all possible groupings of the 18 roses into groups of 6 are equally likely.
(a) What is the probability that the 3 bouquets produced by the assistant each contain exactly two
red roses?
(b) What is the probability that any 2 of the 3 bouquets produced by the assistant contain the
same number of red roses?

Explanation / Answer

(a) The various options for the 6 red roses to go into the 3 bouquets are:

0-0-6 : 3 ways

0-1-5 : 6 ways

0-2-4 : 6 ways

0-3-3 : 3 ways

1-1-4 : 3 ways

1-2-3 : 6 ways

2-2-2 : 1 way

Probability of having two roses in each bouquet = 1/25 = 0.04

(b) In the combinations above, 0-0-6, 0-3-3,1-1-4, 2-2-2 have same number of roles

Probability = (3+3+3+1)/25 = 10/25 = 2/5

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.