Question

A student takes an exam containing 10 multiple choice questions. The probability of choosing a correct answer by knowledgeable guessing is 0.5. If the student makes knowledgeable guesses, what is the probability that he will get between 4 and 8 (both inclusive) questions right? Round your answer to four decimal places.

Answer 1

Solution:

We are given

n = 10

p = 0.5

q = 1 – p = 0.5

We have to find P(4≤X≤8)

P(4≤X≤8) = P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8)

P(X=x) = nCx*p^x*q^(n – x)

P(X=4) = 10C4*0.5^4*0.5^(10 – 4)

P(X=4) = 10C4*0.5^4*0.5^6 = 210*0.5^4*0.5^6 = 0.205078

P(X=5) = 10C5*0.5^5*0.5^5 = 252*0.5^5*0.5^5 = 0.246094

P(X=6) = 10C6*0.5^6*0.5^4 = 210*0.5^6*0.5^4 = 0.205078

P(X=7) = 10C7*0.5^7*0.5^3 = 120*0.5^7*0.5^3 = 0.117188

P(X=8) = 10C8*0.5^8*0.5^2 = 45*0.5^8*0.5^2 = 0.043945

P(4≤X≤8) = P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8)

P(4≤X≤8) = 0.817383

Required probability = 0.8174