Permutation/ Combination: In a quiz, a contestant...

[euro]

In a quiz, a contestant is asked 10 questions, to which he should respond either true or false. He should respond to at least 8 questions correctly to move to the next level of the quiz. If he responds to 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


Official Answer is C

[Rahul@gurome]

He will not proceed to the next level if he responds correctly to seven or less than seven questions.
The probability that he responds correctly to seven or less than seven questions is 1 - (probability that he responds correctly to 8 or more than 8 questions).
Probability that he responds correctly to exactly 8 questions is 10C8*(1/2)^8*(1/2)^2 = 45/1024.
Probability that he responds correctly to exactly 9 questions is 10C9*(1/2)^9*(1/2)^1 = 10/1024.
Probability that he responds correctly to exactly 10 questions is 10C10*(1/2)^10 = 1/1024.
So the probability that he responds correctly to 8 or more than 8 questions is 45/1024 + 10/1024 + 1/1024 = 56/1024.
Or required probability is 1 - 56/1024 = 968/1024 = 121/128.

The correct answer is C.