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

Question

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

IanStewart · Accepted Answer

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

u1983 · Answer

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  .

philipssonicare · Answer

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

Archit3110 · Answer

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

PV66 · Answer

Doesn't look like a 700 question tbh.
You need to pick one couple from the 30 married, which can be done in 30C1 ways. Let's get to the denominator, you need to form a *straight* couple, that means you need to pick 1 from the males and 1 from the females to qualify as a couple. This can be done in 80C1*45C1 ways.

So IMO the probability will be 30/80*45 = 1/120.

Posted from my mobile device

crackGMAT760 · Answer

Bunuel   VeritasKarishma

When they ask for the probability of selecting a couple, why can't we do 60C1 x 2 in the numerator? (60 ways of selecting the first person and then since the person can be either male or female - 2 ways of selecting the first person). If not in this question, can you also please elaborate when can we use this technique.

GMATinsight · Answer

crackGMAT760 60C1*2 = 120 While there are only 30 ways of choosing a couple out of 30 couples. therefore 60C1*2 doesn't have merit. To. make it slightly correct 60C1 = Number of ways of choosing one person out of 30 couples (60 individuals) But now, the second person can be chosen in ONLY 1 WAY because chosen person has only 1 partner who makes couple with chosen one. so you don't need to multiply it by 2 in that case the method will be 60C1*1/(80*45*2) Denominator also must include arrangement if Numerator includes that (60C1 includes arrangement) I hope this help!

nkme2007 · Answer

Chances of selecting a married couple = 30
Chances of selecting a male = 80
Chances of selecting a female = 45

Hence,  probability = 30/(80*45) = 1/120

OA: D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards