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# In a party there were 80 males and 45 females. One pair of a male and

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Intern
Joined: 01 Dec 2018
Posts: 1
In a party there were 80 males and 45 females. One pair of a male and  [#permalink]

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01 Dec 2018, 01:36
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Difficulty:

65% (hard)

Question Stats:

52% (01:44) correct 48% (01:52) wrong based on 73 sessions

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In a party there were 80 males and 45 females. One pair of a male and a female was selected at random for dance, what is the probability that a pair selected is a married couple if there were total 30 married couples in the party?

a) 1/30
b) 1/3600
c) 1/1200
d) 1/120
e) none of these
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Posts: 1806
Re: In a party there were 80 males and 45 females. One pair of a male and  [#permalink]

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01 Mar 2019, 06:14
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Assuming 30 women are married to 30 men: imagine you pick the woman first, then the man. When you pick the woman, you must pick one of the married women to have any hope of getting a married couple. 30/45 = 2/3 of the women are married, so that's the probability our first selection is 'good'. Then once we've picked the married woman, we need to pick the specific man she is married to. There's 1 man she's married to, out of 80 men in total, so a 1/80 probability we pick the 'right' man. Since we need both of these things to happen, we multiply the probabilities:

(2/3) (1/80) = 1/120
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##### General Discussion
Senior Manager
Joined: 15 Feb 2018
Posts: 367
Re: In a party there were 80 males and 45 females. One pair of a male and  [#permalink]

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01 Dec 2018, 01:48
2
This question doesn't work now on account of gay marriage. It requires 30/45 of the females to be married to 30/80 of the males.

2/3·1/80=1/120
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Re: In a party there were 80 males and 45 females. One pair of a male and  [#permalink]

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01 Dec 2018, 11:12
4
As there are 30 couples , the no of ways we can select 1 pair of married couple : 30C1= 30
Now the he no of ways we can select 1 man from 80=80C1= 80
& the he no of ways we can select 1 woman from 45=45C1= 45
Hence , the probability = 30/(80*45)= 1/120............... Ans D.
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In a party there were 80 males and 45 females. One pair of a male and  [#permalink]

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Updated on: 01 Mar 2019, 09:42
1
Male =80 & female= 45

married couple = 30
so
married males; 30 and females 30

we can say
P of married males ; 30/80
and them with females ; 1/45
30/80 * 1/45
IMO 1/120 ; D

Originally posted by Archit3110 on 01 Mar 2019, 05:51.
Last edited by Archit3110 on 01 Mar 2019, 09:42, edited 1 time in total.
In a party there were 80 males and 45 females. One pair of a male and   [#permalink] 01 Mar 2019, 05:51
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