Leaders and Followers

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sat Aug 06, 2011 12:17 pm

At a motivational forum, a group of 1,500 people are separated into two groups, the Leaders and the Followers. 1,000 people are assigned to the Followers and 500 are assigned to the Leaders. Among these people, there are 75 married couples, each consisting of 1 Leader and 1 Follower. If 1 person is chosen randomly from each group, what is the probability that the two people chosen will be a married couple?

3/20000

1/4500

19/1800

1/75

2/225

Source: Beat The GMAT — Problem Solving | Sat Aug 06, 2011 12:17 pm

maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sat Aug 06, 2011 12:30 pm

it shud be: 75/1000*500 = 3/20000

GmatKiss wrote:At a motivational forum, a group of 1,500 people are separated into two groups, the Leaders and the Followers. 1,000 people are assigned to the Followers and 500 are assigned to the Leaders. Among these people, there are 75 married couples, each consisting of 1 Leader and 1 Follower. If 1 person is chosen randomly from each group, what is the probability that the two people chosen will be a married couple?

3/20000

1/4500

19/1800

1/75

2/225

Charged up again to beat the beast

edge: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun Jun 26, 2011 5:45 pm; Thanked: 2 times

by edge » Sat Aug 06, 2011 12:31 pm

My answer is A.

P(married leader) = 75/500 = 3/20
P(married follower) = 75/1000
P(particular married follower) = 1/75 (we need this because we have to find the counterpart of the married leader from the followers)

Therefore, P = 3/20 x 75/1000 x 1/75 = 3/20000.

ajaykpat: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Mon Jun 13, 2011 8:43 am; Thanked: 1 times

by ajaykpat » Sun Aug 07, 2011 3:07 am

from question we have information that each group consisting of 75 couple members.

If first we choose from Leaders group then probability of selecting couple = 75C1 / 500C1

now , for section of couple partner in Followers group we have only one choice i.e. = 1/ 1000C1

combining both probability = 75C1 x 1/ 1000C1 x 500C1 = [spoiler]3/20000[/spoiler]

Br,

ajp

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