A multiple choice test consists of four questions

Question

A multiple choice test consists of four questions, each of which has five choices. Each question has exactly one correct answer.

William guesses randomly at each answer. What is the probability that he gets two or fewer questions correct? (Round your answer to four decimal places.)

Answer 1

Prob ( zero out of four)  + Prob ( 1 out of 4) + P ( 2 out of 4) = (4 choose 0) (0.2)^0 (0.8)^4 +

                                                                                            (4 choose 1) (0.2)^1 (0.8)^3 +

                                                                                            (4 choose 2) (0.2)^2 (0.8)^2

 

 = (0.8)^4 + 4 * (0.2)(0.8)^3 + 6*(0.2)^2 (0.8)^2

 

 = 0.4096 + .4096 +.1536 = 0.9728