Last visit was: 29 Dec 2024, 11:43 It is currently 29 Dec 2024, 11:43
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

A certain business school has 500 students, and the law school at the

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30544
Own Kudos [?]: 36903 [1]
Given Kudos: 26106
Send PM
A certain business school has 500 students, and the law school at the [#permalink] New post   22 Oct 2021, 06:55
Expert Reply
1
Bookmarks
00:00

Question Stats:

44% (01:57) correct 55% (02:49) wrong based on 18 sessions

Hide Show timer Statistics

A certain business school has 500 students, and the law school at the same university has 800 students. Among these students, there are 30 sibling pairs consisting of 1 business student and 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?

A. \(\frac{3}{40000}\)

B. \(\frac{3}{20000}\)

C. \(\frac{3}{4000}\)

D. \(\frac{9}{400}\)

E. \(\frac{6}{130}\)
ShowHide Answer
Official Answer
A
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12239 [0]
Given Kudos: 136
Send PM

Top Member of the Month
Re: A certain business school has 500 students, and the law school at the [#permalink] New post   22 Oct 2021, 07:16
Carcass wrote:
A certain business school has 500 students, and the law school at the same university has 800 students. Among these students, there are 30 sibling pairs consisting of 1 business student and 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?

A. \(\frac{3}{40000}\)

B. \(\frac{3}{20000}\)

C. \(\frac{3}{4000}\)

D. \(\frac{9}{400}\)

E. \(\frac{6}{130}\)



P(selecting a sibling pair) = P(select a business student with a sibling AND select a law student who is that business student's sibling)
= P(select a business student with a sibling) x P(select a law student who is that business student's sibling)
= 30/500 x 1/800
= 30/400,000
= 3/40,000

Answer: A

Note: P(select a business student with a sibling) = 30/500, because 30 of the 500 business students have a sibling in law school.
P(select a law student who is that business student's sibling) = 1/800, because there are 800 law students and only 1 is the sibling of the selected business student.

Cheers,
Brent
avatar
B
Paul121
Manager
Manager
Joined: 19 Jun 2021
Posts: 52
Own Kudos [?]: 27 [0]
Given Kudos: 24
Send PM
Re: A certain business school has 500 students, and the law school at the [#permalink] New post   29 Jul 2023, 05:29
You counted: (30/500)*(1/800)
But what about: (30/800)*(1/500)?

(30/500)*(1/800) + (30/800)*(1/500) = 60/400000 = 3/20000

Answer: B

Why is it wrong?


GreenlightTestPrep wrote:
Carcass wrote:
A certain business school has 500 students, and the law school at the same university has 800 students. Among these students, there are 30 sibling pairs consisting of 1 business student and 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?

A. \(\frac{3}{40000}\)

B. \(\frac{3}{20000}\)

C. \(\frac{3}{4000}\)

D. \(\frac{9}{400}\)

E. \(\frac{6}{130}\)



P(selecting a sibling pair) = P(select a business student with a sibling AND select a law student who is that business student's sibling)
= P(select a business student with a sibling) x P(select a law student who is that business student's sibling)
= 30/500 x 1/800
= 30/400,000
= 3/40,000

Answer: A

Note: P(select a business student with a sibling) = 30/500, because 30 of the 500 business students have a sibling in law school.
P(select a law student who is that business student's sibling) = 1/800, because there are 800 law students and only 1 is the sibling of the selected business student.

Cheers,
Brent
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30544
Own Kudos [?]: 36903 [1]
Given Kudos: 26106
Send PM
Re: A certain business school has 500 students, and the law school at the [#permalink] New post   29 Jul 2023, 05:35
1
Expert Reply
Ben and Lilian are siblings. Ben is studying Business and Lilian is studying Law.
- Possibility of selecting Ben = 1/500
- Possibility of selecting Lilian = 1/800

So the possibility of selecting this specific sibling pair is (1/500) * (1/800) = 1/400,000

Now imagine this concept with the total 30 sibling pairs.

(1/500) * (1/800) * 30 = 30/400,000 = 3/40,000
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30544
Own Kudos [?]: 36903 [1]
Given Kudos: 26106
Send PM
Re: A certain business school has 500 students, and the law school at the [#permalink] New post   29 Jul 2023, 05:35
1
Expert Reply
1st - you need to pick on from any school, who has a sibling
P(l) = 15/500
P(b) = 15/800

2nd - you need to pick his pair sibling from the other school
P(b-l) = 1/800
P9l-b) = 1/500

3rd, you need to multiply resepectively ("AND" - for example - both P(l) and P(b-l) needed) and sum the result ("OR", one of the options needed)

1. 15/500*1/800 = 15/400,000
2. 15/800*1/500 = 15/400,000


1+2. = 15/400,000 +15/400,000 = 30/400,000 = 3/40,000
avatar
B
Paul121
Manager
Manager
Joined: 19 Jun 2021
Posts: 52
Own Kudos [?]: 27 [0]
Given Kudos: 24
Send PM
Re: A certain business school has 500 students, and the law school at the [#permalink] New post   29 Jul 2023, 06:53
Cab you please explain the first part of this approach?
P(l) = 15/500
P(b) = 15/800

Why did you put 15 students in each school?
It talks about 30 pairs of siblings, so there are 60 students.
So each school has 30 students who have siblings in the other school, no?

Thank you for the help, I just confused by the 15 number.

Carcass wrote:
1st - you need to pick on from any school, who has a sibling
P(l) = 15/500
P(b) = 15/800

2nd - you need to pick his pair sibling from the other school
P(b-l) = 1/800
P9l-b) = 1/500

3rd, you need to multiply resepectively ("AND" - for example - both P(l) and P(b-l) needed) and sum the result ("OR", one of the options needed)

1. 15/500*1/800 = 15/400,000
2. 15/800*1/500 = 15/400,000


1+2. = 15/400,000 +15/400,000 = 30/400,000 = 3/40,000
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30544
Own Kudos [?]: 36903 [1]
Given Kudos: 26106
Send PM
Re: A certain business school has 500 students, and the law school at the [#permalink] New post   29 Jul 2023, 07:12
1
Expert Reply
Because they treat a couple as one

or you can think this way

probability of selecting sibling 30 students from b school 30/500
probability of selecting sibling 30 students from law school 30/800
probability that selected sibling students are members of the same sibling pair 1/30
(30/500)*(30/800)*(1/30) = 3/40000
Prep Club for GRE Bot
gmatclubot
Re: A certain business school has 500 students, and the law school at the [#permalink]
29 Jul 2023, 07:12
Moderators:
adewale223
GRE Instructor
88 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1116 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact