GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jun 2019, 00:59

### 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
Your Progress

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

# a family has 5 children, what is the probability that there are 3 boys

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2942
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
a family has 5 children, what is the probability that there are 3 boys  [#permalink]

### Show Tags

10 Sep 2018, 22:35
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:35) correct 44% (02:00) wrong based on 33 sessions

### HideShow timer Statistics

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

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Joined: 02 Aug 2018
Posts: 2
Re: a family has 5 children, what is the probability that there are 3 boys  [#permalink]

### Show Tags

10 Sep 2018, 22:40
1
Probability of a girl or a boy = 1/2
Total children = 5
Probability = 1/2*1/2*1/2*1/2*1/2----1

Now Seq is BBBGG.

So it can be arranged in 5!/3!*2! Ways. ----2

Taking 1 and 2 together

1/32 * 5!/3!*2! = 10/32 = 5/16

Hence E is the answer

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 7752
Re: a family has 5 children, what is the probability that there are 3 boys  [#permalink]

### Show Tags

10 Sep 2018, 22:55
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

Source: http://www.GMATinsight.com

each child could be in two ways - B or G so two ways
total ways of the 5 child = $$2*2*2*2*2 = 2^5=32$$

ways 3 out of 5 are B = $$5C3=\frac{5!}{3!2!}=10$$

probability =$$\frac{10}{32}=\frac{5}{16}$$

E
_________________
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936
a family has 5 children, what is the probability that there are 3 boys  [#permalink]

### Show Tags

11 Sep 2018, 06:03
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

Source: http://www.GMATinsight.com

$$? = P\left( {3B\,\,{\text{and}}\,\,2G\,\,{\text{among}}\,\,5\,\,{\text{children}}} \right)$$

First Step: evaluate the probability of one "typical" favorable scenario,
> Say BBBGG :: 1/(2^5) = 1/32

Second Step: check whether all favorable scenarios are EQUIPROBABLE.
> They are: BBGBG, ... , GGBBB all have this same probability (each one considered separately, of course.)

Third Step: check how many favorable scenarios are there.
> There are C(5,3) = 10 scenarios, because we have to choose 3 places (among 5) to "put" the letter B.
Note that C(5,3) = C(5,2) because choosing 3 places (among 5) to "put" B is equivalent to choosing 2 places to "put" G.

Four Step: check if all scenarios of the previous step are MUTUALLY EXCLUSIVE, so that we can ADD their probabilities next!
> Yes. When (say) BBBGG occurs, BGBBG does not occur... the same applies to any 2 occurrences among the 10 of the Third Step!

Fifth Step: taking into account everything previously considered,
$$? = C\left( {5,3} \right) \cdot \frac{1}{32} = \frac{10}{32} = \frac{5}{16}$$

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

Regards,
fskilnik.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
a family has 5 children, what is the probability that there are 3 boys   [#permalink] 11 Sep 2018, 06:03
Display posts from previous: Sort by

# a family has 5 children, what is the probability that there are 3 boys

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne