Question

a multiple choice quiz in six sigma green belt 11 consists of 10 questions each of which has five possible answers of which only one is correct. a student passes the quiz if six or more correct answer obtained. what is the probability of passing the quiz if on each question, a student can eliminate three incorrect answers and then guess between the remaining two.

Answer 1

There are total 10 questions and 6 or more to be answered correctly to pass the test.

each question has 5 options out of which 3 incorrect are eliminated.

probability of selecting a correct answer from 2 is 1/2 = 0.5

P(X = r) = nCr * p^r * (1-p)^(n-r)

probability that 6 or more answered correctly,
P(X >= 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
= 10C6 * 0.5^6 * 0.5^4 + 10C7 * 0.5^7 * 0.5^3 + 10C8 * 0.5^8 * 0.5^2 + 10C9 * 0.5^9 * 0.5^1 + 10C10 * 0.5^10 * 0.5^0

= 0.377