It is currently 20 Nov 2017, 12:28

GMAT 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

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

Practice
Pays

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In a room filled with 7 people, 4 people have exactly 1

Author Message
TAGS:

Hide Tags

Current Student
Joined: 11 Oct 2013
Posts: 121

Kudos [?]: 67 [0], given: 137

Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31
In a room filled with 7 people, 4 people have exactly 1 [#permalink]

Show Tags

11 Dec 2015, 03:50
In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?

A. 5/21
B. 3/7
C. 4/7
D. 5/7
E. 16/21

This is how I solved.

Case 1: The group of 4 have exactly 1 sibling. So maximum 2 people can be picked from that group who are not siblings.
Case 2: The group of 3 has 2 siblings each. So maximum only 1 person from the group can be chosen.
Total number of ways in which we can pick people is 7C2 = 21.

Case 1 -
$$2C1 * 2C1$$ ways

Case 2 -
$$3C1 * 4C1$$ ways

Probability -
$$\frac{2C1 * 2C1 + 4C1 * 3C1}{21} = \frac{16}{21}$$

Experts, please confirm if my approach is correct

+Kudos if this helped!
_________________

Its not over..

Kudos [?]: 67 [0], given: 137

Manager
Joined: 31 Dec 2016
Posts: 91

Kudos [?]: 11 [0], given: 22

In a room filled with 7 people, 4 people have exactly 1 [#permalink]

Show Tags

12 Aug 2017, 11:49
lagomez wrote:
You have people 1-2-3-4-5-6-7

4 have exactly 1 sibling which can mean:
1-2 are siblings
3-4 are siblings

3 have exactly 2 siblings which can mean:
5-6-7 are siblings

The probability of picking 1 is (1/7)
The probability of not getting a sibling pair is (5/6) because the only other sibling is 2
Therefore, if 1 is selected first the probability of not getting a sibling pair is 5/42
Multiply that by 4 because the probability is the same whether you start with 1-2-3-4 so you get 20/42 for the first 4 people

Now let's go to the group of 3:
The probability of picking 5 is (1/7)
The probability of not getting a sibling pair is (4/6) which the non-sibling pair is 1-2-3-4
Therefore the probability is 4/42. Multiply that probability by 3, which represent 5-6-7 so the probability is 12/42

Now you have two probabilities: 12/42 and 20/42
add both and you get 32/42 or 16/21

It's easier to use the complement. Not sure why people are trying so hard here to use the choose formula when it makes the question 1000X harder

4/7 chance to pick a person with 1 sibling * 1/6 chance you get a sibling or 4/42

3/7 change to pick a 2 person sibling * 2/6 or 6/42

Total of 10/42 of getting a sibling.

We get to use the simple or rule not the generalized since the things are mutually exclusive. And we aren't drawing twice just once. So either a 4 person is picked first or 3 person.

So that simplifies to 5/21 then 1 minus this is 16/21 for the odds that they are not siblings. 5/21 they are.

Kudos [?]: 11 [0], given: 22

Intern
Joined: 27 Sep 2017
Posts: 3

Kudos [?]: 5 [0], given: 2

Re: In a room filled with 7 people, 4 people have exactly 1 [#permalink]

Show Tags

02 Oct 2017, 22:38
lagomez Can you explain how you got 5/6?

Kudos [?]: 5 [0], given: 2

Re: In a room filled with 7 people, 4 people have exactly 1   [#permalink] 02 Oct 2017, 22:38

Go to page   Previous    1   2   3   [ 43 posts ]

Display posts from previous: Sort by