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

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Manager
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An exam consists of 8 true/false questions. Brian forgets to [#permalink]  23 Jul 2014, 21:18
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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
[Reveal] Spoiler: OA
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Posts: 77
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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]  23 Jul 2014, 21:34
1
KUDOS
maggie27 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

Since 70% is the passing rate, .70 ( 8 questions) = 5.6 correct answers (or 6 rounded up)

We must then look for the probability of passing:

All correct answers = $$\frac{1}{2}^8=\frac{1}{256}$$

7 correct answers = $$\frac{8C1}{1/2^8} = \frac{8}{256}$$

6 correct answers = $$\frac{8C2}{1/2^8} = \frac{28}{256}$$

$$\frac{1}{256}+\frac{8}{256}+\frac{28}{256}=\frac{37}{256}$$

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An exam consists of 8 true/false questions. Brian forgets to [#permalink]  24 Jul 2014, 07:49
maggie27 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

I am not sure if the wording of the question is accurate. Anyone else feels the same way?

There are only two possibilities - Either Brian fails or he passes. So, probability that Brian passes = 1/2

Did I read the question incorrectly or is the wording ambiguous?
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An exam consists of 8 true/false questions. Brian forgets to [#permalink]  24 Jul 2014, 07:56
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Expert's post
Game wrote:
maggie27 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

I am not sure if the wording of the question is accurate. Anyone else feels the same way?

There are only two possibilities - Either Brian fails or he passes. So, probability that Brian passes = 1/2

Did I read the question incorrectly or is the wording ambiguous?

No, that's not correct. According to your logic the probability of me dating Charlize Theron is also 1/2. Either yes or no. Wish this was true.
_________________
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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]  24 Jul 2014, 17:20
Bunuel wrote:
Game wrote:
maggie27 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

I am not sure if the wording of the question is accurate. Anyone else feels the same way?

There are only two possibilities - Either Brian fails or he passes. So, probability that Brian passes = 1/2

Did I read the question incorrectly or is the wording ambiguous?

No, that's not correct. According to your logic the probability of me dating Charlize Theron is also 1/2. Either yes or no. Wish this was true.

OK. Got it.
On a side note, probability of you dating Charlize Theron is 0 & here is the mathematical explanation for the math expert:

Assuming Charlize Theron (C.T.) will date only one person at a time
Probability(Game dating C.T.) + Probability(Bunuel dating C.T.) + ... = 1
Since Probability(Game dating C.T.) = 1
Probability(Bunuel dating C.T.) + ... = 1 - 1 = 0
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An exam consists of 8 true/false questions. Brian forgets to [#permalink]  09 Aug 2014, 14:54
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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) 5/32
(D) 219/256
(E) 15/16

Intern
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Posts: 39
Concentration: Marketing, Strategy
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GMAT 2: 680 Q47 V36
WE: Marketing (Transportation)
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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]  09 Aug 2014, 16:02
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) 5/32
(D) 219/256
(E) 15/16

If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.

If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.

So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.
Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.

The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 37/256.

I know there is a shorter way, but this is how I did it in about 2:34
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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]  10 Aug 2014, 00:35
2
KUDOS
If you have True or False question, then each question has a $$\frac{1}{2}$$ chance of getting correct.

If a passing score is 70% it means Brian needs to get right or 6 questions (6/8=75%), or 7 questions (7/8=87.5%), or 8 questions (8/8=100%).

The probability to have all 8 questions right is: $$\frac{1}{2^8}$$
The probability to have 7 questions right and 1 wrong is: $$C_8^1*\frac{1}{2^7}*\frac{1}{2}=\frac{8}{2^8}$$ (choose this incorrect answer $$C_8^1$$, probability to have 7 right $$\frac{1}{2^7}$$, and probability to have 1 wrong $$\frac{1}{2}$$)
The probability to have 6 questions right and 2 wrong is: $$C_8^2*\frac{1}{2^6}*\frac{1}{2^2}=\frac{28}{2^8}$$ (choose the se 2incorrect answers $$C_8^2$$, probability to have 6 right $$\frac{1}{2^6}$$, and probability to have 2 wrong $$\frac{1}{2^2}$$)

The probability is $$\frac{1}{2^8}+\frac{8}{2^8}+\frac{28}{2^8}=\frac{37}{256}$$
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I'm happy, if I make math for you slightly clearer
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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]  14 Dec 2014, 04:06
Bunuel wrote:
Game wrote:
maggie27 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

I am not sure if the wording of the question is accurate. Anyone else feels the same way?

There are only two possibilities - Either Brian fails or he passes. So, probability that Brian passes = 1/2

Did I read the question incorrectly or is the wording ambiguous?

No, that's not correct. According to your logic the probability of me dating Charlize Theron is also 1/2. Either yes or no. Wish this was true.

I have a very basic and silly doubt
Why the probability of getting 7 right is 8c1/(1/2^8)

I mean i understood the denominator part but why 8c1?
As it has to be 7 answers out of 8... So i thought it will be 2^7/2^8

Math Expert
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Posts: 27000
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Kudos [?]: 40035 [0], given: 5397

Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]  15 Dec 2014, 06:26
Expert's post
gauriranjekar wrote:
I have a very basic and silly doubt
Why the probability of getting 7 right is 8c1/(1/2^8)

I mean i understood the denominator part but why 8c1?
As it has to be 7 answers out of 8... So i thought it will be 2^7/2^8

Because 7 correct out of 8 can occur in 8 ways:
YYYYYYYN (first 7 correct and 8th not).
YYYYYYNY
YYYYYNYY
YYYYNYYY
YYYNYYYY
YYNYYYYY
YNYYYYYY
NYYYYYYY
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Posts: 27000
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Kudos [?]: 40035 [0], given: 5397

Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]  26 Jan 2015, 03:28
Expert's post
maggie27 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

VERITAS PREP OFFICIAL SOLUTION:

First, Brian must get 70% of the 8 questions right to pass. 70% of 8 is 5.6, though, so he must get 6 questions right (there's no such thing as "partial credit" on a true/false question). This leaves us with three possible outcomes:

6 right, 2 wrong

7 right, 1 wrong

8 right, 0 wrong

We can use our knowledge of permutations with identical elements to calculate the probability here since, for our purposes, a correct answer on the first question is the same as a correct answer on the third question. Thus, there are 8!/(6!2!), or 28, ways to get 6 questions right, 8!/7!, or 8, ways to get 7 questions right, and only 1 way to get all 8 of the questions right. Brian has a total of 37 good outcomes. The number of possible outcomes, though, is 2^8, or 256, giving Brian a 37/256 chance of passing. Good luck, Brian!

_________________
Re: An exam consists of 8 true/false questions. Brian forgets to   [#permalink] 26 Jan 2015, 03:28
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