Problem Solving

In a quiz, a contestant is asked 10 questions, to which he should answer true or false. He should answer at least 8 questions correctly to move to the next level of the quiz. If he answers all the questions, what is the probability that he does not proceed to the next level?
(A)7/128
(B)17/28
(C)121/128
(D)11/28
(E)10/128

This problem has been bugging me all day. A detailed explanation would be highly appreciated. OA is C

Hi,
Each question can be either T or F.
So, total number of different sets of answers is 2^10
Number of ways of getting 8 correct is choosing 8 correct options from 10, i.e. 10C8 = 45
Number of ways of getting 9 correct is choosing 9 correct options from 10, i.e. 10C9 = 10
Number of ways of getting all correct is = 1
So, probability of passing is (1+10+45)/2^10 = 56/1024 = 7/128
So, probability that he does not proceed is 1- (7/128) = 121/128

Hence, C

Hi Frank,

I understood that there 2^10 possible answers..

Now what i have NOT understood is how 10C8 is the way of getting 8 correct answers.

For each Question the answer might be true or False, both have equal probability to become correct.

In my opinion 10C8 is way of answering 8 questions out of 10.

I have a question of how this is the way of getting correct answers for 8 questions.. Please help ..

Frankenstein wrote:Hi,
Each question can be either T or F.
So, total number of different sets of answers is 2^10
Number of ways of getting 8 correct is choosing 8 correct options from 10, i.e. 10C8 = 45
Number of ways of getting 9 correct is choosing 9 correct options from 10, i.e. 10C9 = 10
Number of ways of getting all correct is = 1
So, probability of passing is (1+10+45)/2^10 = 56/1024 = 7/128
So, probability that he does not proceed is 1- (7/128) = 121/128

Hence, C

finites wrote:Hi Frank,

I understood that there 2^10 possible answers..

Now what i have NOT understood is how 10C8 is the way of getting 8 correct answers.
For each Question the answer might be true or False, both have equal probability to become correct.
In my opinion 10C8 is way of answering 8 questions out of 10.
I have a question of how this is the way of getting correct answers for 8 questions.. Please help ..

Hi,
Let me elaborate this:
A question can be made correct in only 1 way right?
Similarly a question can be made incorrect in only 1 way right?
Now, let us pick 8 questions. These 8 questions will be correct in only 1 way right(all those 8 questions should match the key)?
Now, these 8 questions can be picked from 10 in 10C8 ways right?
So, the number of ways of making 8 questions right is (Number of ways of picking 8 questions)*(number of ways of making those 8 questions right) = 10C8*1 = 10C8.
If you still feel I haven't explained well, let me know at which specific point you didn't understand so that I can explain better.

got it now