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by MBA.Aspirant » Sun Jun 19, 2011 10:39 pm
Tony's political science final exam consists of eight True/False questions. If Tony guesses on every question, what is the probability that he gets exactly seven questions right?

A) 1/32
B) 1/16
C) 1/8
D) 7/8
E) 31/32
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by Frankenstein » Sun Jun 19, 2011 10:46 pm
Hi,
Each question can be either T or F. So, total number of possible answers is 2^8
For seven questions to be right, 1 option should be wrong. So, any of the wrong questions can be made incorrect by choosing the opposite option (i.e T instead of F and vice-versa) in 1 way
Question that can be made incorrect can be chosen in 8C1 ways.
So, probability is 8C1.1/2^8 = 1/32

Hence, A
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by MBA.Aspirant » Sun Jun 19, 2011 11:06 pm
Frankenstein wrote:Hi,
Each question can be either T or F. So, total number of possible answers is 2^8
For seven questions to be right, 1 option should be wrong. So, any of the wrong questions can be made incorrect by choosing the opposite option (i.e T instead of F and vice-versa) in 1 way
Question that can be made incorrect can be chosen in 8C1 ways.
So, probability is 8C1.1/2^8 = 1/32

Hence, A
Thanks Frankesnstein for ur help. I don't get the highlighted part. I get that we have 2^8 answer choices to choose from. We need to know the probability of getting exactly 7 right answers out of, can you explain this part? Thanks
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by Frankenstein » Sun Jun 19, 2011 11:15 pm
Okay.. Out of those 8 questions we have to make 1 question incorrect right?
That incorrect question can be either 1st,2nd, 3rd ...8th right?
So, we can make 7 questions right in 8 ways right?
For example:
If the answer key for the question paper is T,T,T,T,T,T,T,T
We can have 7 questions correct in 8 ways:
1)F,T,T,T,T,T,T,T
2)T,F,T,T,T,T,T,T
3)T,T,F,T,T,T,T,T
4)T,T,T,F,T,T,T,T
5)T,T,T,T,F,T,T,T
6)T,T,T,T,T,F,T,T
7)T,T,T,T,T,T,F,T
8)T,T,T,T,T,T,T,F

That is essentially picking 1 question from the 8 questions to make it incorrect - 8C1 ways
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by MBA.Aspirant » Mon Jun 20, 2011 12:01 am
so basically the probability of getting 7 right is the probability of getting 1 wrong and this can happen in 8 ways, right? so out of the 2^8 possible answers, there're 8 ways an answer can be wrong or 7 can be right.

8/2^8 = 1/2^5

Thanks for explaining.
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