probability problem...kinda tricky

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