BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2505
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

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

by BTGmoderatorLU » Fri May 04, 2018 1:56 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

The OA is E.

Please, can anyone assist me with this PS question? I'm confused with it. Thanks in advance!
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
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 May 04, 2018 2:05 pm
BTGmoderatorLU wrote: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
First we need to recognize that the given information tells us that the 7 people consist of:
- a sibling trio
- a sibling pair
- and another sibling pair

Using counting techniques:

For this question, it's easier to find the complement.
So P(not siblings) = 1 - P(they are siblings)

P(they are siblings) = [# of ways to select 2 siblings] / [total # of ways to select 2 people]

# of ways to select 2 siblings
Case a) 2 siblings from the sibling trio: from these 3 siblings, we can select 2 siblings in 3C2 ways (3 ways)
Case b) 2 siblings from first sibling pair: we can select 2 siblings in 2C2 ways (1 way)
Case c) 2 siblings from second sibling pair: we can select 2 siblings in 2C2 ways (1 way)

So, total number of ways to select 2 siblings = 3+1+1 = 5

total # of ways to select 2 people
We have 7 people and we want to select 2 of them
We can accomplish this in 7C2 ways (21 ways)

So, P(they are siblings) = 5/21

This means P(not siblings) = 1 - 5/21
= 16/21

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Fri May 04, 2018 5:44 pm
Hi All,

Brent's approach focuses on the use of the Combination Formula, which is probably the most "elegant" way to solve this problem. There are other ways to solve this problem though, if you're not yet comfortable with doing that type of math. Here's an option that focuses on straight "probability math"....

The first step is to organize the 7 people into family-groups. 4 people have exactly 1 sibling. We'll call those people:

A1, A2
B1, B2

A1 and A2 are siblings, etc.

3 people have exactly 2 siblings. We'll call them:

C1, C2 and C3

We're going to select 2 people from the room; what is the probability that they are NOT siblings.

Probability = (# of ways you want something to happen)/(# of total possibilities)

The total number of possibilities = (7)(6) = 42

Now let's figure out the ways that give us 2 non-siblings:

If the first person selected is:
A1, then there are 5 non-sibling options
A2, then there are 5 non-sibling options
B1, then there are 5 non-sibling options
B2, then there are 5 non-sibling options
C1, then there are 4 non-sibling options
C2, then there are 4 non-sibling options
C3, then there are 4 non-sibling options

The total number of 2 non-sibling options is 5+5+5+5+4+4+4 = 32

The probability is 32/42 = 16/21

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat May 05, 2018 2:14 am
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?
5/21
3/7
4/7
5/7
16/21
Let's say that the 7 people are ABCDEFG.

4 people have exactly 1 sibling:
Let's say that A and B are siblings and that C and D are siblings.
This means:
A has 1 sibling (B).
B has 1 sibling (A).
C has 1 sibling (D).
D has 1 sibling (C).

3 people have exactly 2 siblings:
Let's say that E, F and G are all siblings of each other.
This means:
E has 2 siblings (F and G).
F has 2 siblings (E and G).
G has 2 siblings (E and F).

Total number of sibling pairs = 5: AB, CD, EF, EG, FG.
Total number of pairs that can be formed from 7 people: 7C2 = 21.
P(sibling pair) = 5/21
P(not sibling pair) = 1 - 5/21 = 16/21.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Legendary Member
Posts: 2499
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

by swerve » Sat May 05, 2018 7:45 am
That is one way, I think it is easier to calculate the probabilities than the combinations.

there is 4/7 chance of selecting a person with one sibling initially with a 5/6 probability the second person will not be a sibling.

There is a 3/7 Chance of selecting a person with 2 siblings initially with 4/6 probability the second person will not be a sibling.

Simply adding these probabilities together gives you the answer.

4/7 * 5/6 + 3/7 * 4/6 = 20/42 + 12/42 = 32/42 = 16/21.

Regards!
Top
Post new topic Post Reply
• Page 1 of 1