Aishwarya1204 wrote:A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts 2 flowers together at random in a bouquet. However, the customer calls and says that she does not want 2 of the same flower. What is the probability that the florist does not have to change the bouquet?
Answer is : [spoiler] 13/18 [/spoiler]
First, we can rewrite the question as
"What is the probability that the two flowers are different colors?"
Well, P(diff colors) = 1 -
P(same color)
Aside: let A = azalea, let B = buttercup, let P = petunia
P(same color) = P(both A's
OR both B's
OR both P's)
= P(both A's)
+ P(both B's)
+ P(both P's)
Now let's examine each probability:
P(both A's):
We need the 1st flower to be an azalea and the 2nd flower to be an azalea
So, P(both A's) = (2/9)(1/8) = 2/72
P(both B's)
= (3/9)(2/8) = 6/72
P(both P's)
= (4/9)(3/8) = 12/72
So,
P(same color) = (2/72) + (6/72) + (12/72) = 20/72 =
5/18
Now back to the beginning:
P(diff colors) = 1 -
P(same color)
= 1 -
5/18
= [spoiler]13/18[/spoiler]
Cheers,
Brent
