A student has taken an exam consisting 10 multiple choice questions. Each question has 4 answer choices and has one correct answer. Questions are independent of each other. If the student answer questions randomly, what is the probability that the student marks less than 3 correct choices?

Answer 1

p correct = .25
1-p = .75

p(0 correct)= C(10,0).25^0*.75^10

p(1 correct)= C(10,1).25^1 *.75^9

p(2 correct)= C(10,2).25^2 *.75^8

c(10,0) = 1 of course
C(10,1) = 10
C(10,2) = 45

add the three probabilities

C(10,1)