The probability

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TuanNguyen87: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed May 25, 2011 9:40 am

by TuanNguyen87 » Wed Jun 08, 2011 4:57 pm

A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the propability that the 2 students will be a sibling pair?

A. 3/40,000
B. 1/3,600
C. 9/2,000
D. 1/60
E. 1/15

Answer: A

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jun 08, 2011 5:22 pm

TuanNguyen87 wrote:A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the propability that the 2 students will be a sibling pair?

A. 3/40,000
B. 1/3,600
C. 9/2,000
D. 1/60
E. 1/15

Answer: A

Thanks a lot everyone!

Required probability = No. of favorable outcome/ Total no. of outcomes
Total no. of outcomes = 800C1 * 1000C1
There are 60 sibling pairs, so no. of favorable outcomes = 60
Therefore, Required probability = = 60/(800*1000) = 3/40,000

The correct answer is A.

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g.shankaran: Master | Next Rank: 500 Posts; Posts: 101; Joined: Tue Oct 27, 2009 8:19 amFollowed by: 2 members; Thanked: 4 times

by g.shankaran » Wed Jun 08, 2011 5:22 pm

TuanNguyen87 wrote:A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the propability that the 2 students will be a sibling pair?

A. 3/40,000
B. 1/3,600
C. 9/2,000
D. 1/60
E. 1/15

Answer: A

Thanks a lot everyone!

If 1 student is to be selected at random from each class, what is the propability that the 2 students will be a sibling pair?

junior class = 1000 stu
senior class = 800 stu

There are 60 sibling pairs. so each class has 60 students who are siblings.

selecting 1 student from junior class who is a sibling is 60C1 = 60
selecting 1 student from junior class = 1000C1 = 1000

selecting 1 student from senior class who is a sibling is 1 ( We have already selected a student from junior class. so there will be only one student in the senior class who is a sibling of the student selected from junior class)
selecting 1 student from senior class = 800C1 = 800

so, probability = 60/1000 * 1/800 = 3/40000 Hence A

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Wed Jun 08, 2011 5:22 pm

probability that we select any (good) student from the first (any) group is either 60/1000 or 60/800
probability that the second student we select from the group will also be good (sibling) is either 1/800 or 1/1000

i used two alternatives above to show that it does not matter from which group we select first

60/1000 * 1/800
60/800 * 1/1000

both are giving 3/40,000 a

TuanNguyen87 wrote:A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the propability that the 2 students will be a sibling pair?

A. 3/40,000
B. 1/3,600
C. 9/2,000
D. 1/60
E. 1/15

Answer: A

Thanks a lot everyone!

Success doesn't come overnight!

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Wed Jun 08, 2011 8:08 pm

total J=1000,total S=800
60 sibling pairs(1J,1S)
Total pairs = 1 from J and 1 from S = 1000*800
prob = 60/800000 = 3/40000
IMO A

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phanideepak: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Wed Apr 27, 2011 6:13 amFollowed by: 2 members; Location: Hyderabad; Thanked: 10 times; GMAT Score:730

by phanideepak » Wed Jun 08, 2011 8:22 pm

Since there are 60 sibling pairs we have 60 students in Junior class and 60 students in senior class who are siblings.

probability of selecting a sibling pair = (60/1000)(1/800) = 3/40000

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Wed Jun 08, 2011 8:54 pm

OA A - 3/40000

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Wed Jun 08, 2011 11:06 pm

Thanks for the post.

I chose C as I have incorrectly counted the number of siblings instead of sibling pairs.

Thanks for the learning.

Regards,

Pranay

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu Feb 22, 2018 5:05 pm

TuanNguyen87 wrote:A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the propability that the 2 students will be a sibling pair?

A. 3/40,000
B. 1/3,600
C. 9/2,000
D. 1/60
E. 1/15

The probability of selecting any one sibling from the 60 sibling pairs in the junior class 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, the probability of selecting any one sibling from the 60 sibling pairs in the senior class 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

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