marble

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ruplun: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jun 18, 2010 7:09 amFollowed by: 2 members; Thanked: 1 times

by ruplun » Thu Jun 30, 2011 11:09 am

In a bag of marbles, there are 3 red,2 white and 5 blue.If Bob takes 2 marbles out of the bag, what is the probability that he will have one white and one blue marble?

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Source: Beat The GMAT — Problem Solving | Thu Jun 30, 2011 11:09 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu Jun 30, 2011 11:27 am

Hi,
3R, 2W, 5B.
2 balls can be picked from 10 in 10C2 = 45ways
1W and 1B can be picked in 2C1*5C1 = 10 ways
So, probability = 10/45 = 2/9

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Thu Jun 30, 2011 11:28 am

ruplun wrote:In a bag of marbles, there are 3 red,2 white and 5 blue.If Bob takes 2 marbles out of the bag, what is the probability that he will have one white and one blue marble?

there're 10 marbles

Prob. of getting 1 white and 1 blue = 2/10 * 5/9 + 5/10 * 2/9 = 2/9

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ntamhane: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Thu Jun 30, 2011 4:15 amFollowed by: 1 member; Thanked: 1 times

by ntamhane » Thu Jun 30, 2011 6:27 pm

As there are 10 Marbles and 2 need to be selected its 10!/8!*2!=45 ways
The wining situation is 1 White and 1 Blue
So 1 white can be selected in 2!/1!*1! = 2ways
and 1 blue can be selected in 5!/4!*1! = 5 ways
therefore 5*2=10
so the probability of the wining situation is 10/45 = 2/9

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Thu Jun 30, 2011 9:38 pm

probability of white ball = 2/10
probability of taking a blue ball = 5/9. similarly vice versa for taking a blue ball first and then a white ball.

hence 2* 2/10 * 5/9 = 2/9

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