Roses and Carnations

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Wed Feb 17, 2010 6:05 am

In a garden, 40% of the flowers are roses and rest are carnations. If 1/4th of the roses and 1/10th of carnations are red, find the probability that a red flower selected at random is rose.

A.6/9
B.6/8
C.1/17
D.5/8
E.7/9

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Feb 17, 2010 6:23 am

harsh.champ wrote:In a garden, 40% of the flowers are roses and rest are carnations. If 1/4th of the roses and 1/10th of carnations are red, find the probability that a red flower selected at random is rose.

A.6/9
B.6/8
C.1/17
D.5/8
E.7/9

P(red/rose)= 1/4, P(red/carnation)=1/10.
P(Rose/red) = [P(red/rose) x P(rose)]/[P(red/carnation) x P(carnation) +P(red/rose) x P(rose)]
=[1/4x.4]/[1/4x.4+1/10x.6]=[1/10]/[1/10+3/50]=[spoiler]5/8 D[/spoiler]

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sadullaevd: Senior | Next Rank: 100 Posts; Posts: 81; Joined: Wed Apr 08, 2009 3:12 pm; Location: South Korea; Thanked: 4 times

by sadullaevd » Wed Feb 17, 2010 6:24 am

Let 100 be the number of flowers in the garden.

40 roses, 60 carnations,

1/4 of 40= 10 red roses, 1/10 of 60 = 6 red carnations,

probability of red roses= number of red roses/(red roses + red carnations)

P= 10/16

p=5/8

should be D.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Roses and Carnations

by Scott@TargetTestPrep » Fri Feb 05, 2021 2:51 pm

harsh.champ wrote: ↑
Wed Feb 17, 2010 6:05 am
In a garden, 40% of the flowers are roses and rest are carnations. If 1/4th of the roses and 1/10th of carnations are red, find the probability that a red flower selected at random is rose.

A.6/9
B.6/8
C.1/17
D.5/8
E.7/9

Solution:

We can let the number of flowers be 100. So there are 40 roses and 60 carnations. Of the 40 roses, 10 are red, and of the 60 carnations, 6 are red. Therefore, the probability that a red flower selected at random is a rose is 10/(10 + 6) = 10/16 = 5/8.

Answer: B

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