A student randomly guesses the correct answer in a multiple choice quiz of 10 question. If each question has 5 choices, what is the probability the student gets exactly 7 correct? What is the probability the students gets more than 7 correct?
this binary ... correct (c) or wrong (w)
... p(c) = 1/5 = .2 ... p(w) = 4/5 = .8
(c + w)^10 = c^10 + 10 c^9 w + 45 c^8 w^2 + 120 c^7 w^3 + ... + w^10
(c + w)^10 = .2^10 + (10 * .2^9 * .8) + (45 * .2^8 * .8^2) + (120 * .2^7 * .8^3)
p(exactly 7 correct) is the 4th term of the expansion
p(more than 7 correct) is the sum of the 1st three terms