The repeated guessing of correct answers from multiple choice questions are Bernoulli trials. Let X represent the number of correct answers by guessing in the set of 5 multiple choice questions.
Probability of getting a correct answer is , p=13
∴q=1−p=1−13=23
Clearly, X has a binomial distribution with n=5 and p=13
∴P(X=x)=nCxqn−xpx
=5Cx(23)5−x⋅(13)x
P(guessingmorethan4correctanswers)=P(X≥4)
=P(X=4)+P(X=5)
=5C4(23)⋅(13)4+5C5(13)5
=5⋅23⋅181+1⋅1243
=10243+1243
=11243