GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 18 Feb 2020, 08:05

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.

Close

Request Expert Reply

Confirm Cancel

A test has 5 multiple-choice questions. Each question has 4 answer opt

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 28 Jan 2017
Posts: 26
Reviews Badge CAT Tests
A test has 5 multiple-choice questions. Each question has 4 answer opt  [#permalink]

Show Tags

New post 09 Jan 2020, 18:42
3
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

36% (02:57) correct 64% (02:12) wrong based on 14 sessions

HideShow timer Statistics

A test has 5 multiple-choice questions. Each question has 4 answer options (A,B,C,D). What is the probability that a student will choose “B” for at least four questions if no questions are left blank?

A) 1/256
B) 5/1024
C) 1/64
D) 21/1024
E) 1/16
CrackVerbal Quant Expert
User avatar
G
Joined: 12 Apr 2019
Posts: 385
Re: A test has 5 multiple-choice questions. Each question has 4 answer opt  [#permalink]

Show Tags

New post 10 Jan 2020, 01:31
In this question on probability, we need to understand two things:
#1 – Any of the four/five questions can have the answer as B, so we need to select those four/five questions.
#2 – The probability of getting B as the right answer is ¼ and that of not getting B as the right answer is ¾.

The number of ways of selecting any 4 questions of 5 = \(5_C_4\) = 5. In each of these 5 cases, the probability that the student will choose B as an answer is ¼ and the probability that he will not choose B is ¾.
Therefore, probability that the student will choose B for 4 questions = 5 * \((\frac{1}{4})^4\) * (\(\frac{3}{4}\)) = \(\frac{15 }{ 1024}\).

The number of ways of selecting all 5 questions of 5 = \(5_C_5\) = 1.
Therefore, probability that the student will choose B for all 5 questions = 1 * \((\frac{1}{4})^5\) * \((\frac{3}{4})^0\) = \(\frac{1 }{ 1024}\).

The total probability =\( \frac{15 }{ 1024}\) + \(\frac{1 }{ 1024}\) = \(\frac{16 }{ 1024}\) = \(\frac{1 }{ 64}\).
The correct answer option is C.

Hope that helps!
_________________
GMAT Club Bot
Re: A test has 5 multiple-choice questions. Each question has 4 answer opt   [#permalink] 10 Jan 2020, 01:31
Display posts from previous: Sort by

A test has 5 multiple-choice questions. Each question has 4 answer opt

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





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