euro wrote: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
Official Answer is C
My Explanation:
Let R - right answer and W - wrong answer
P(R) = 1/2 and P(W) = 1/2
First find P1, the probability of his proceeding to the next level.
P1 = either exactly 2 questions wrong OR exactly 1 question wrong OR zero question wrong
Case of exactly 2 question wrong:
RRRRRRRRWW - probability of this sequence = ((1/2)^10)
total possible arrangement of this sequence = ((!10)/(!8*!2)) -----taking help of anagram-ism.
P(exactly 2 question wrong) = ((1/2)^10) * ((!10)/(!8*!2))
Case of exactly 1 question wrong:
RRRRRRRRRW - probability of this sequence = ((1/2)^10)
total possible arrangement of this sequence = ((!10)/(!9*!1)) -----taking help of anagram-ism.
P(exactly 1 question wrong) = ((1/2)^10) * ((!10)/(!9*!1))
Case of zero question wrong:
RRRRRRRRRR - probability of this sequence = ((1/2)^10)
total possible arrangement of this sequence = ((!10)/(!10)) =1
P(zero question wrong) = ((1/2)^10)
P1 = (((1/2)^10) * ((!10)/(!8*!2)) ) + (((1/2)^10) * ((!10)/(!9*!1)) ) + ((1/2)^10)) [adding the three cases]
=((1/2)^10)[45 + 10 + 1]
=56/1024
=7/128
i.e probability of his proceeding to the next level, P1 = 7/128
Therefore, probability that he does not proceed to the next level = 1- probability that he proceed to the next level
=1-(7/128)
121/128
CORRECT ANSWER - C
