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01 Dec 2018, 01:36
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D
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Difficulty:
55%
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Question Stats:
59% (01:43) correct
41%
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wrong
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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
a) 1/30
b) 1/3600
c) 1/1200
d) 1/120
e) none of these
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
(2/3) (1/80) = 1/120
01 Dec 2018, 11:12
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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.
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.
