probability

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rtaha2412: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Fri Nov 27, 2009 7:48 pm; Thanked: 1 times

by rtaha2412 » Wed Jan 05, 2011 10:15 am

A flower shop has 2 tulips, 2 roses, 2 daisies, and 2 lilies. If two flowers are sold at random, what is the probability of not picking exactly two tulips?

a 1/8
b 1/7
c 1/2
d 7/8
e 27/28

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Source: Beat The GMAT — Problem Solving | Wed Jan 05, 2011 10:15 am

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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 Jan 05, 2011 10:19 am

rtaha2412 wrote:A flower shop has 2 tulips, 2 roses, 2 daisies, and 2 lilies. If two flowers are sold at random, what is the probability of not picking exactly two tulips?

a 1/8
b 1/7
c 1/2
d 7/8
e 27/28

Probability of picking exactly two tulips = (Probability of picking a tulip out of 8 flower)*(Probability of picking a tulip out of remaining 7) = (2/8)*(1/7) = 1/28
Probability of not picking exactly two tulips = 1 - 1/28 = 27/28

The correct answer is E.

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Wed Jan 05, 2011 10:39 am

rtaha2412 wrote:A flower shop has 2 tulips, 2 roses, 2 daisies, and 2 lilies. If two flowers are sold at random, what is the probability of not picking exactly two tulips?

a 1/8
b 1/7
c 1/2
d 7/8
e 27/28

Method 1 : Using Probability :
P(not picking exactly 2 tulips) = 1 - P(picking exactly 2 tulips) = 1 - (2/8)*(1/7) = 27/28

Method 2 :Using Permutations and combinations
Total no. of ways in which 2 flowers can be chosen = 8C2 = 28
Total no. of ways in which not exactly two tulip flowers are chosen =Total - no. of ways in which exactly 2 tulips flowers are chosen = 28 - 1 = 27

So, required probability = 27/28

E

Thanks
Anshu

(Every mistake is a lesson learned )

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