OG 10 Problem 432 on Page 134 - Probability - The Beat The GMAT Forum

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OG 10 Problem 432 on Page 134 - Probability

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weipei: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sat Jun 17, 2006 3:41 pm

OG 10 Problem 432 on Page 134 - Probability

by weipei » Sat Jan 27, 2007 2:42 am

I don't understand the explanation from the back of the book. Can someone plz explain the answers?

Thanks a bunch!

problem 432 on OG 10.

A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. 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. 1/3600
c. 9/2000
d. 1/60
e. 1/15

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Source: Beat The GMAT — Problem Solving | Sat Jan 27, 2007 2:42 am

Neo2000: Legendary Member; Posts: 519; Joined: Sat Jan 27, 2007 7:56 am; Location: India; Thanked: 31 times

by Neo2000 » Sat Jan 27, 2007 8:02 am

IF there are 60pairs, it means there are 60students in the senior class who have a sibling in the junior class.

In order to pick 1 pair, select 1 student fm the senior class who has a sibling
This can be done in 60/800 ways
This student has only 1 sibling in the junior class and can be picked in 1/1000ways

So total number of ways = (60/800) * (1/1000)

Hope this helps

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

by BTGmoderatorRO » Fri Oct 06, 2017 5:37 pm

The probability of an event to occur is defined as , p(E) = (number of required outcome)/(number of total outcome)
probability of two events, A and B occurring at the same time is define as p(A) and p(B)= p(A) * p(B)

now, the number of junior students, n(j) = 1000
and number of senior students, n(s) = 800
There are sixty siblings pair, each from both classes.
i.e 60 students from the junior class have one sibling each in the same class.
let p(j) be the probability of a junior student having a sibling in the senior class.

p(j) = (no. of junior students that have a sibling) / (total number of junior students)
= 60/1000 = 3/50
Also, let P(s) be the probability of a senior class student having a sibling in the junior class

therefore, p(S)= 60/800 = 3/40
Now, the probability of one junior student and one senior student being sibling
= p(J) and p(S)
= p(J) * p(S)
= (3/50) * (3/40)
= 9/2000

Hence, option C is very correct :mrgreen:

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GMAT/MBA Expert

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

by Brent@GMATPrepNow » Fri Oct 06, 2017 5:46 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 probability that the 2 students selected will be a sibling pair?

A) 3/40,000
B) 1/3,600
C) 9/2,000
D) 1/60
E) 1/16

One option is to apply probability rules.

So, for two siblings to be selected, 2 things must happen: we must select a junior who has a senior sibling AND the senior selected must be the sibling of the selected junior.
We get P(junior with sibling AND selected senior is sibling to selected junior)= P(junior with sibling) x P(selected senior is sibling to selected junior)

P(junior with sibling): there are 1000 juniors and 60 of them have senior siblings. So, P(junior with sibling)=60/1000

P(selected senior is sibling to selected junior): Once the junior has been selected, there is only 1 senior (out of 800 seniors) who is the sibling to the selected junior. So, P(selected senior is sibling to selected junior)= 1/800

So, the probability is (60/1000)x(1/800) = 3/40,000
The answer is A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: OG 10 Problem 432 on Page 134 - Probability

by Scott@TargetTestPrep » Fri Jan 24, 2020 3:10 pm

weipei wrote: ↑
Sat Jan 27, 2007 2:42 am
I don't understand the explanation from the back of the book. Can someone plz explain the answers?

Thanks a bunch!

problem 432 on OG 10.

A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs, each consisting of 1 junior and 1 senior. 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. 1/3600
c. 9/2000
d. 1/60
e. 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

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