Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 May 2016, 05:40
GMAT Club Tests

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In a multiple choice test comprising 5 Questions, each with

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

Hide Tags

Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 368
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Followers: 10

Kudos [?]: 299 [0], given: 50

Reviews Badge
In a multiple choice test comprising 5 Questions, each with [#permalink]

Show Tags

New post 07 Aug 2012, 06:58
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

66% (03:33) correct 34% (03:01) wrong based on 50 sessions

HideShow timer Statistics

In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.

A) 24/256
B) 53/512
C) 105/512
D) 459/512
E) 47/256
[Reveal] Spoiler: OA

_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33098
Followers: 5782

Kudos [?]: 70965 [0], given: 9857

Re: In a multiple choice test comprising 5 Questions, each with [#permalink]

Show Tags

New post 07 Aug 2012, 08:02
Expert's post
1
This post was
BOOKMARKED
SOURH7WK wrote:
In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.

A) 24/256
B) 53/512
C) 105/512
D) 459/512
E) 47/256


The probability of getting correct (C) answer is 1/4 and the the probability of getting wrong (W) answer is 3/4.

We need to find the probability of getting at 3, 4 or 5 correct answers:

The probability of getting 3 correct answers out of 5 is \(\frac{5!}{3!2!}*(\frac{1}{4})^3*(\frac{3}{4})^2\), we are multiplying by \(\frac{5!}{3!2!}\) since CCCWW scenario can occur in several ways: CCCWW, WWCCC, CWCWC, ... basically the number of permutations of 5 letters CCCWW, out of which 3 C's and 2 W's are identical (\(\frac{5!}{3!2!}\));

The probability of getting 4 correct answers out of 5 is \(\frac{5!}{4!}*(\frac{1}{4})^4*(\frac{3}{4})\);

The probability of getting 5 correct answers out of 5 is simply \((\frac{1}{4})^5\).

The overall probabity will be the sum of the above probabilities: \(\frac{5!}{3!2!}*(\frac{1}{4})^3*(\frac{3}{4})^2+\frac{5!}{4!}*(\frac{1}{4})^4*(\frac{3}{4})+(\frac{1}{4})^5=\frac{53}{512}\).

Answer: B.

P.S. Not a GMAT type of qustion.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 776 [0], given: 43

Re: In a multiple choice test comprising 5 Qs, each with 4 choic [#permalink]

Show Tags

New post 07 Aug 2012, 08:06
SOURH7WK wrote:
In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.

A) 24/256
B) 53/512
C) 105/512
D) 459/512
E) 47/256


We can compute either the probability of answering 3, 4, or 5 questions correctly, or subtract from 1 the probability of answering 0, 1, or 2 questions.
The probability of answering any question correctly is 1/4, and obviously, answering incorrectly is 3/4.

P(3 correct answers) =\(\frac{5*4}{2}(\frac{1}{4})^3(\frac{3}{4})^2=\frac{90}{4^5}\)
P(4 correct answers) =\(5(\frac{1}{4})^4(\frac{3}{4})=\frac{15}{4^5}\)
P(5 correct answers) =\((\frac{1}{4})^5=\frac{1}{4^5}\)
The sum of the above probabilities gives \(\frac{106}{4^5}=\frac{53}{512}\).

Answer B

Relevant topic for this question - Binomial probability distribution
Being a straightforward technical question, I question its importance for a real test.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
avatar
Joined: 15 Apr 2012
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 8

Re: In a multiple choice test comprising 5 Questions, each with [#permalink]

Show Tags

New post 07 Aug 2012, 08:16
Here is my approach-
Probability for choosing correct answer is 1/4 and incorrect answer is 3/4
For 3 correct answers,
C(5,3)*(1/4)^3*(3/4)^2=90/(4^5)
For 4 correct answers,
C(5,4)*(1/4)^4*(3/4)^1=15/(4^5)
For 5 correct answers,
C(5,5)*(1/4)^5*(3/4)^0=1/(4^5)

So total probability
=106/1024

=53/512
Ans B
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9719
Followers: 466

Kudos [?]: 120 [0], given: 0

Premium Member
Re: In a multiple choice test comprising 5 Questions, each with [#permalink]

Show Tags

New post 23 Dec 2015, 23:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

SVP
SVP
avatar
Joined: 17 Jul 2014
Posts: 1615
Location: United States
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.56
WE: General Management (Transportation)
Followers: 10

Kudos [?]: 164 [0], given: 104

GMAT ToolKit User Premium Member Reviews Badge
Re: In a multiple choice test comprising 5 Questions, each with [#permalink]

Show Tags

New post 18 Mar 2016, 19:59
SOURH7WK wrote:
In a multiple choice test comprising 5 Questions, each with 4 choices, what is the probability of a student getting 3 or more questions correct? Each question has only one correct answer and the student is equally likely to choose any of the four choices.

A) 24/256
B) 53/512
C) 105/512
D) 459/512
E) 47/256


we need to find the probability when:
3 questions are answered correctly, 2 incorrectly
4 correctly, 1 incorrectly
and 5 correctly.

1 case: (1/4)^3 * (3/4)^2 = 9/1024. since we have 5 questions, and we need to select 3 out of these, we can answer correctly 3 out of 5 in 5C3 ways. or total probability 90/1024
2 case: (1/4)^3 * (3/4) = 3/1024. we can answer 4 correctly in 5C4 ways. total probability 15/1024
3 case: (1/4)^5. we can answer all 5 correctly in 1 way. so 1/1024

total: 90+15+1/1024 = 106/1024 = 53/512

B
Re: In a multiple choice test comprising 5 Questions, each with   [#permalink] 18 Mar 2016, 19:59
    Similar topics Author Replies Last post
Similar
Topics:
10 Experts publish their posts in the topic A certain multiple-choice math quiz contains five questions, each with Bunuel 5 23 Apr 2015, 03:43
In a multiple choice test there are 65 questions each having calmkeeper 1 12 Dec 2013, 05:46
Experts publish their posts in the topic A multiple choice test consists of 4 questions, and each que mirzahamza 5 06 Nov 2013, 10:57
4 Experts publish their posts in the topic In a Question paper there are 4 multiple choice questions avaneeshvyas 6 18 Oct 2012, 13:54
2 Experts publish their posts in the topic In an examination comprising 20 questions, each question has Smita04 1 25 Jul 2012, 23:43
Display posts from previous: Sort by

In a multiple choice test comprising 5 Questions, each with

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.