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# At a motivational forum, a group of 1,500 people are separated into tw

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Director
Joined: 12 Feb 2015
Posts: 966
At a motivational forum, a group of 1,500 people are separated into tw  [#permalink]

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19 Nov 2019, 23:39
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Difficulty:

45% (medium)

Question Stats:

50% (02:20) correct 50% (02:48) wrong based on 18 sessions

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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?

A) $$\frac{3}{20,000}$$

B) $$\frac{1}{4,500}$$

C) $$\frac{19}{1,800}$$

D) $$\frac{1}{75}$$

E) $$\frac{1}{20}$$

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Manish

"Only I can change my life. No one can do it for me"
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Joined: 16 Feb 2015
Posts: 177
Location: United States
Concentration: Finance, Operations
Re: At a motivational forum, a group of 1,500 people are separated into tw  [#permalink]

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19 Nov 2019, 23:59
1
CAMANISHPARMAR 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?

A) $$\frac{3}{20,000}$$

B) $$\frac{1}{4,500}$$

C) $$\frac{19}{1,800}$$

D) $$\frac{1}{75}$$

E) $$\frac{1}{20}$$

Explanation

Method 1

P(married leader) = 75/500 = 3/20
P(married follower) = 75/1000
P(particularly 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

Method 2

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

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

now, for a 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 = 3/20000

Pls give kudos, If you find my explanation good enough
Re: At a motivational forum, a group of 1,500 people are separated into tw   [#permalink] 19 Nov 2019, 23:59
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# At a motivational forum, a group of 1,500 people are separated into tw

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