A quiz constists of 20 multiplechoice questions each with po

A quiz constists of 20 multiple-choice questions, each with possible answers for someone who makes random guesses for all of the answers. Find the probability of passing if the minimum passing grad is 50 peresentage P(pass) =

Solution

Propability of passing one question out of 5 opitons = 1/5

so propability of passing p = 1/5 = 0.2

so propability of failure q = 1-p = 1-0.2 = 0.8

so no as it says 50% means out of 20 only 10 questions are minimum grade to pass

so the probability of \'x\' success in \'n\' trials is nCx

SO Probability P = nCx p^x q^(n-x)

Here 50% imples x= 10

so P(X=10) = 20C10 * (0.2)^10 (0.8)^10

= 20! / 10!(20-10)! * (0.2)^10 (0.8)^10 note nCx = n!/x!(n-x)!

={ (20 * 19*17*18*16*15*14*13*12*11* 10! )/10! *10! } *(0.0000001024) * (0.107374)

= 184756**(0.0000001024) * (0.107374)

= 0.0020314

so P(pass) = 0.0020314.