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An exam consists of 8 true/false questions. Brian forgets to [#permalink]
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23 Jul 2014, 22:18
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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
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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]
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23 Jul 2014, 22:34
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 + 7 correct answers + 6 correct answers = 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 = \(\frac{8C2}{1/2^8} = \frac{28}{256}\) \(\frac{1}{256}+\frac{8}{256}+\frac{28}{256}=\frac{37}{256}\) Answer is B



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An exam consists of 8 true/false questions. Brian forgets to [#permalink]
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24 Jul 2014, 08:49
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]
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24 Jul 2014, 08:56



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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]
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24 Jul 2014, 18:20
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]
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09 Aug 2014, 15:54
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
Could anyone please explain?



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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]
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09 Aug 2014, 17:02
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
Could anyone please explain?
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]
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10 Aug 2014, 01:35
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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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]
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14 Dec 2014, 05:06
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 Please help..!!



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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]
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15 Dec 2014, 07:26



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Re: An exam consists of 8 true/false questions. Brian forgets to [#permalink]
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26 Jan 2015, 04:28
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! Answer: B.
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