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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

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

by BTGModeratorVI » Wed Apr 22, 2020 11:04 am

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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

Answer: B
Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Wed Apr 22, 2020 11:04 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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

by Brent@GMATPrepNow » Sun Apr 26, 2020 10:03 am

BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:04 am
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

Answer: B
Source: Veritas Prep

Let's say that you have NO IDEA how to solve this question (many students will face this predicament).

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.

Brian needs to correctly guess at least 6 of the 8 questions .
How likely does that FEEL?
Well, if you feel the likelihood is less than 50%, then we can eliminate C, D and E.

Great! In 10 seconds, we're down to a 50-50 guess between A and B.

Now, 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.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8087; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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

by Scott@TargetTestPrep » Sun May 03, 2020 5:32 am

BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:04 am
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

Answer: 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

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