Probability and Combination

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Aishwarya1204: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Oct 14, 2012 1:08 am

by Aishwarya1204 » Fri Oct 19, 2012 11:09 pm

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]

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Source: Beat The GMAT — Problem Solving | Fri Oct 19, 2012 11:09 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Oct 19, 2012 11:19 pm

I posted two different approaches here:

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Aishwarya1204: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Oct 14, 2012 1:08 am

by Aishwarya1204 » Fri Oct 19, 2012 11:30 pm

GMATGuruNY wrote:I posted two different approaches here:

https://www.beatthegmat.com/probability- ... 15290.html

Thank you so much. Sorry for repeating the question !

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Oct 20, 2012 6:34 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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