Probability1

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gunjan1208: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Jul 28, 2011 12:48 amFollowed by: 6 members; Thanked: 28 times

by gunjan1208 » Wed Oct 05, 2011 12:39 am

Please help me explaning the answer (Source MGMAT strategy guides)

A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts two flowers together at
random in a bouquet. However, the customer calls and says that she does not want
two of the same flower. What is the probability that the florist does not have to
change the bouquet?

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Source: Beat The GMAT — Problem Solving | Wed Oct 05, 2011 12:39 am

sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Wed Oct 05, 2011 12:52 am

P(2 azaleas) = 2/9C2 ; P(2 Buttercup) = 3/9C2; P(2 Petunias) = 4C2/9C2

1 - P(Bouquet with identical flowers) = P(bouquet having 2 different flowers)

2/72+6/72+12/72 = 20/72

1-5/18 = 13/18

Last edited by sl750 on Wed Oct 05, 2011 10:25 am, edited 1 time in total.

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svd.kumar: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Tue Sep 21, 2010 7:38 am; Thanked: 4 times

by svd.kumar » Wed Oct 05, 2011 10:11 am

Please post the correct answer, I got a different result. Please correct me if I am wrong

2 azaleas, 3 buttercups, and 4 petunias

Probability of selecting 2 azaleas = 2/9*1/8
Probability of selecting 3 buttercups = 3/9*2/8
Probability of selecting 4 petunias = 4/9*3/8

Which gives 2/72 + 6/72 + 12/72 = 5/18

But we want probability of not having exactly same = 1 - 5/18 = 13/18

Cheers,
SVD

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Wed Oct 05, 2011 10:23 am

I guess I screwed up. 2C2 = 1

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Oct 05, 2011 8:03 pm

gunjan1208 wrote:Please help me explaning the answer (Source MGMAT strategy guides)

A florist has 2 azaleas, 3 buttercups, and 4 petunias. She puts two flowers together at
random in a bouquet. However, the customer calls and says that she does not want
two of the same flower. What is the probability that the florist does not have to
change the bouquet?

Let azaleas = A, buttercups = B, and petunias = P

Required probability = 1 - [Probability of both being A + probability of both being B + probability of both being P]
Probability of choosing the same flower = 2/9 * 1/8 + 3/9 * 2/8 + 4/9 * 3/8 = 5/18

Therefore, required probability = 1 = 5/18 = [spoiler]13/18[/spoiler]

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Wed Oct 05, 2011 8:05 pm

Probability at its most basic is want over total - so eventually we want to solve for

(bouquet without two same)/ All bouquets

First solve for how many bouquets can you make - with two flowers you have 9 to choose from for the first slot and 8 to choose from in the second slot but order doesn't matter so you divide by 2. Thus 9*8/2 = 36 total bouquets.

Now we need to find the nubmer of bouquets that won't have the same - there ways to look at this
Bouquet has an azalea and another flower (2 x 7)/2 = 7 bouquets
or
Bouquet has a buttercup and another flower: (3 x 6)/2 = 9 bouquets
or
Bouquet has a petunia and another flower: (4 x 5)/2 = 10 bouquets.

add up all bouquets that don't have double flowers - 26 options.

Now put you want over your total - for 26/36 = 13/18 is the final answer

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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gunjan1208: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Jul 28, 2011 12:48 amFollowed by: 6 members; Thanked: 28 times

by gunjan1208 » Thu Oct 06, 2011 2:35 am

Probability of choosing the same flower = 2/9 * 1/8 + 3/9 * 2/8 + 4/9 * 3/8 = 5/18

Why do we multiply with these boldenend numbers?

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catfreak: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Fri Jul 16, 2010 1:24 pm; Thanked: 1 times

by catfreak » Thu Oct 06, 2011 7:57 am

gunjan1208 wrote:Probability of choosing the same flower = 2/9 * 1/8 + 3/9 * 2/8 + 4/9 * 3/8 = 5/18

Why do we multiply with these boldenend numbers?

We are choosing two flower out of 9 one after the other.
So for say buttercup first flower can be chosen in 3/9 and the next buttercup flower after the fist is removed will be chosen in 2/8.

The same logic applies for the rest of the flowers.

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