On a typical scantron exam, there are 4 choices for each problem (a, b, c, or d). If you are given an exam with 6 problems and you guessed randomly, what is them probability of getting at least half the problems right?

Answer 1

so you want 2 right + 3 right + 4 right

prob(correct guess) = 1/4
prob(wrong guess) = 3/4

prob as stated
= C(4,2)(1/4)^2 (3/4)^2 + C(4,3) (1/4)^3 (3/4)^1 + C(4,4)(1/4)^4 (3/4)^0
= 6(1/16)(9/16) + 4(1/64)(3/4) + 1/256
= 67/256