GMAT Official Guide - Probability googly - The Beat The GMAT Forum

GMAT Official Guide - Probability googly

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Sat Apr 07, 2007 12:35 am

A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of one junior and one senior student. if 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair.

1) 3/40,000

2) 1/3,600

3) 9/2000

4) 1/60

5) 1/15

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Source: Beat The GMAT — Problem Solving | Sat Apr 07, 2007 12:35 am

Princeton Review: GMAT Instructor; Posts: 22; Joined: Fri Mar 16, 2007 10:28 pm

by Princeton Review » Sat Apr 07, 2007 5:31 am

When you're thinking about probability, the common sense way to consider it is "what I want" / "total possible".

For this problem, the ultimate outcome that you want is to pick a sibling pair from among the juniors and seniors. So what has to happen for that outcome to occur?

First, from among the juniors you have to pick someone who has a sibling in the senior class. There are 60 of those, so the chances of that event are 60/1000, or 6/100

Next, you have to pick that peron's sibling from among the seniors. There is only going to be one person in the senior class who will be the sibling of whomever you picked from the junior class, so that will give you 1/800.

Multiply those together and you get 6/80,000. This reduces to 3/40,000.

Matt McIver

Princeton Review Instructor

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Sun Sep 16, 2018 2:00 pm

Cybermusings wrote:A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of one junior and one senior student. if 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair.

1) 3/40,000

2) 1/3,600

3) 9/2000

4) 1/60

5) 1/15

\[\left( J \right)\,\,{\text{Junior}}\,\,:\,\,\,1000\,\,{\text{students}}\,\,,\,\,\,{J_1}\,,\,{J_2},\,\, \ldots \,\,,\,\,{J_{60}}\,\,{\text{among}}\,\,{\text{them}}\,\,\,\left( {{\text{the}}\,\,{\text{ones}}\,\,{\text{with}}\,\,{\text{senior}}\,\,{\text{siblings}}} \right)\]
\[\left( S \right)\,\,{\text{Senior}}\,\,:\,\,\,800\,\,{\text{students}}\,\,,\,\,\,{S_1}\,,\,{S_2},\,\, \ldots \,\,,\,\,{S_{60}}\,\,{\text{among}}\,\,{\text{them}}\,\,\,\left( {{\text{the}}\,\,{\text{ones}}\,\,{\text{with}}\,\,{\text{junior}}\,\,{\text{siblings}}} \right)\]
\[\left( {{J_1}\,,\,{S_1}} \right)\,\,;\,\,\left( {{J_2}\,,\,{S_2}} \right)\,\,;\,\, \ldots \,\,;\,\,\left( {{J_{60}}\,,\,{S_{60}}} \right)\,\,\,:\,\,\,{\text{pairs}}\,\,{\text{of}}\,\,{\text{siblings}}\,\]

\[? = P\left( {{\text{pair}}\,{\text{of}}\,{\text{siblings}}\,,\,\,{\text{in}}\,{\text{one}}\,J\,{\text{and}}\,{\text{one}}\,S\,{\text{extraction}}} \right)\]

\[{\text{Total}}\,\,:\,\,\,1000 \cdot 800\,\,\,{\text{equiprobables}}\,\,\,\left[ {\left( {{J_m},{S_n}} \right)\,\,,\,\,\,{\text{where}}\,\,1 \leqslant m \leqslant 1000\,\,{\text{and}}\,\,\,1 \leqslant n \leqslant 800} \right]\]
\[{\text{Favorable}}\,\,:\,\,60\,\,\,\,\,\left[ {\left( {{J_k},{S_k}} \right)\,\,,\,\,\,{\text{where}}\,\,1 \leqslant k \leqslant 60} \right]\,\,\,\,\]
\[? = \frac{{60}}{{1000 \cdot 800}} = \underleftrightarrow {\frac{{4 \cdot 15}}{{1000 \cdot 4 \cdot 200}}} = \frac{{4 \cdot 3 \cdot 5}}{{1000 \cdot 4 \cdot 5 \cdot 40}} = \frac{3}{{40 \cdot 1000}}\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Sep 18, 2018 5:53 pm

Cybermusings wrote:A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of one junior and one senior student. if 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair.

1) 3/40,000

2) 1/3,600

3) 9/2000

4) 1/60

5) 1/15

In the junior class, the probability of selecting any one sibling from the 60 sibling pairs is 60/1000. Once that person is selected, the probability of selecting his or her sibling from the senior class is 1/800; thus, the probability of a selecting a sibling pair is:

60/1000 x 1/800 = 3/50 x 1/800 = 3/40000

Alternatively, in the senior class, the probability of selecting any one sibling from the 60 sibling pairs is 60/800. Once that person is selected, the probability of selecting his or her sibling from the junior class is 1/1000; thus, the probability of a selecting a sibling pair is:

60/800 x 1/1000 = 3/40 x 1/1000 = 3/40000

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Sep 19, 2018 6:40 am

Cybermusings wrote:A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of one junior and one senior student. if 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair.

A) 3/40,000

B) 1/3,600

C) 9/2000

D) 1/60

E) 1/15

P(selecting a sibling pair) = P(select a junior with a sibling AND select the senior who is that junior's sibling)
= P(select a junior with a sibling) x P(select the senior who is that junior's sibling[/u])
= 60/1000 x 1/800
= 60/800,000
= 3/40,000
= A

Note: P(select a junior with a sibling) = 60/1000, because 60 of the 1000 juniors have a sibling who is a senior.
P(select a senior who is that junior's sibling) = 1/800, because there are 800 senior's and only 1 of them is the sibling of the selected junior.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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