Question

If you make random guesses for 20 multiple choice test questions each with four possible answers, what is the probability of

a) Getting at least one correct (5 points)

         b) Getting all answers wrong; (5 points)

Answer 1

Number of questions = n = 20

Number of possible answers = 4

P[ Answer is correct ] = 1/4

P[ Answer is not correct ] = 1 - P[ Answer is correct ]

P[ Answer is not correct ] = 1 - 1/4

P[ Answer is not correct ] = 3/4

P[ Getting at least one correct ] = 1 - P[ Getting all answers wrong ]

P[ Getting all answers wrong ] = P[ Answer is not correct ]^n ( as the answer of one question is independent of other )

P[ Getting all answers wrong ] = (3/4)^20

P[ Getting all answers wrong ] = 0.0032

P[ Getting at least one correct ] = 1 - 0.0032

P[ Getting at least one correct ] = 0.9968