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

Redeem

a family has 5 children, what is the probability that there

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

a family has 5 children, what is the probability that there

by GMATinsight » Mon Sep 10, 2018 9:48 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

a family has 5 children, what is the probability that there are 3 boys and 2 girls among the children?

A) 1/32
B) 1/16
C) 3/32
D) 1/4
E) 5/16

Source: www.GMATinsight.com

Answer: Option E
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
Source: — Problem Solving |
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 » Tue Sep 11, 2018 4:25 am
The problem should make clear that P(boy) = P(girl) = 1/2:
A family has 5 children. If each child is equally likely to be a boy or a girl, what is the probability that there are 3 boys and 2 girls among the children?

A) 1/32
B) 1/16
C) 3/32
D) 1/4
E) 5/16
P(exactly n times) = P(one way) * total possible ways.

Let B = boy and G = girl.

P(one way):
One way to get exactly 3 boys and 2 girls is BBBGG.
P(BBBGG) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32.

Total possible ways:
Any arrangement of the letters BBBGG will yield exactly 3 boys and 2 girls.
Thus, to account for all the ways to get exactly 3 boys and 2 girls, the result above needs to be multiplied by the number of ways to arrange BBBGG.
Number of ways to arrange BBBGG = 5!/(3!2!) = 10.

Multiplying the results above, we get:
P(exactly 3 boys and 2 girls) = 10 * 1/32 = 10/32 = 5/16.

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
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

A family has 5 children, what is the probability that there

by fskilnik@GMATH » Tue Sep 11, 2018 4:39 am
A family has 5 children. If each child is equally likely to be a boy or a girl, what is the probability that there are 3 boys and 2 girls among the children?

A) 1/32
B) 1/16
C) 3/32
D) 1/4
E) 5/16

Source: www.GMATinsight.com
\[? = P\left( {3B\,\,{\text{and}}\,\,2G\,\,{\text{among}}\,\,5\,\,{\text{children}}} \right)\]

Imagine 3 B´s and 2 G´s in a row... each sequence is associated with the children´s sexuality, from (say) the older to the younger child.

Total number: 2^5 = 32 equiprobable sequences (for instance starting with BBBBB and ending with GGGGG.)

Favorable number: C(5, 3) = 10 , because we must choose among the 5 positions in the sequence, 3 of them to "put" the B´s (and the remaining 2 to "put" the G´s).

\[? = \frac{{C\left( {5,3} \right)}}{{32}} = \frac{{10}}{{32}} = \frac{5}{{16}}\]

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

Regards,
fskilnik.
Last edited by fskilnik@GMATH on Wed Sep 26, 2018 2:18 pm, edited 1 time in total.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top

GMAT/MBA Expert

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

by Scott@TargetTestPrep » Wed Sep 12, 2018 5:46 pm
GMATinsight wrote:a family has 5 children, what is the probability that there are 3 boys and 2 girls among the children?

A) 1/32
B) 1/16
C) 3/32
D) 1/4
E) 5/16
The number of 5 children of any GMAT is 2 x 2 x 2 x 2 x 2 = 2^5 = 32. The number of ways that the 5 children could be 3 boys and 2 girls is 5!/(3! x 2!) = (5 x 4)/2! = 10. Therefore, the probability is 10/32 = 5/16.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1