An exam consists of 8 true/false questions. Brian forgets to

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

An exam consists of 8 true/false questions. Brian forgets to

by BTGmoderatorDC » Thu Sep 05, 2019 5:30 pm

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An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes?

A) 1/16
B) 37/256
C) 1/2
D) 219/256
E) 15/16

OA B

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Thu Sep 05, 2019 5:30 pm

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by [email protected] » Thu Sep 05, 2019 8:30 pm

Hi All,

We're told that an exam consists of 8 true/false questions and that Brian forgets to study (so he must guess blindly on each question) and that any score above 70% is a passing grade. We're asked for the probability that Brian passes?

To start, since there are 8 questions that each have 2 possible outcomes, there are 2^8 = 256 possible arrangements of answers to those 8 questions. Since....

5/8 = 62.5%
6/8 = 75%

...Brian must get AT LEAST 6 of the 8 question correct to pass. Thus, we have to determine the total number of ways to get 6, 7 or 8 answers correct. This can be done with the Combination Formula.

8c6 = (8)(7)/(2)(1) = 28 possible ways to get 6 correct
8c7 = (8)/(1) = 8 possible ways to get 7 correct
8c8 = 1 possible ways to get 8 correct

Total = 28 + 8 + 1 = 37 of the 256 possible outcomes.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu Sep 05, 2019 9:50 pm

BTGmoderatorDC wrote:An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes?

A) 1/16
B) 37/256
C) 1/2
D) 219/256
E) 15/16

OA B

Source: Veritas Prep

Given that the passing mark is 70%, Brian must get 70% of 8 = 5.6 questions correct. Since the number of questions is an integer, Brian must have at least 6 questions correct. Or, he must get 6, 7, or 8 questions correct.

Number of ways to get 6 out of 8 questions correct = 8C6 = 8!/(6!*2!) = 28;
Number of ways to get 7 out of 8 questions correct = 8C7 = 8!/(7!*1!) = 8;
Number of ways to get 8 out of 8 questions correct = 8C8 = 1

Total number of ways to get at least 6 questions correct = 28 + 8 + 1 = 37
Total number of ways to get any number of questions correct (None to all 8) = 2^8 = 256 (Each question has two choices: True/False)

Thus, the probability that Brian passes = 37/256

The correct answer: B

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Fri Sep 06, 2019 4:45 am

BTGmoderatorDC wrote:An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes?

A) 1/16
B) 37/256
C) 1/2
D) 219/256
E) 15/16

OA B

Source: Veritas Prep

Let's say that you have NO IDEA how to solve this question.
The great thing about probability questions is that, even if you don't know how to answer them, you can often eliminate some answers by using your gut instincts alone.

As Rich and Jay noted (above), Brian needs to correctly guess at least 6 of the 8 questions.
How likely does that FEEL?
Well, if should feel less than 50% likely, which means we can eliminate C, D and E.
Great, in 10 seconds, we're down to a 50-50 guess between A and B.

Guess A or B and move on knowing that you just added a lot of time to your "time bank" that you can devote to other questions.

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: 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 » Mon Sep 09, 2019 6:25 pm

BTGmoderatorDC wrote:An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes?

A) 1/16
B) 37/256
C) 1/2
D) 219/256
E) 15/16

OA B

Source: Veritas Prep

Since 70% of 8 is 5.6, Brian must answer at least 6 questions correctly in order to pass the exam.

The probability that he answers exactly 6 questions correctly is:

8C6 x (1/2)^6 x (1/2)^2 = 28 x (1/2)^8 = 28/256

The probability that he answers exactly 7 questions correctly is:

8C7 x (1/2)^7 x (1/2)^1 = 8 x (1/2)^8 = 8/256

The probability that he answers all 8 questions correctly is:

8C8 x (1/2)^8 x (1/2)^0 = 1 x (1/2)^8 = 1/256

Therefore, the probability that he answers at least 6 questions correctly is:

28/256 + 8/256 + 1/256 = 37/256

Answer: B

Scott Woodbury-Stewart
Founder and CEO
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