A multiple choice test contains 12 questions, 8 of which have 4 answers each to choose from and 4 of which have 5 answers to choose from. If a student randomly guesses all of his answers, what is the probability that he will get exactly 2 of the 4 answer questions correct and at least 3 of the 5 answer questions correct? ANS: 0.2552 Heres what I did: Out of the 8-four answer questions, the student gets 2 of them = (8C2) Out of the 4-five answer questions, the student gets 3 of them = (4C3) Therefore: [8C2(.25)^2(.75)^6][ 4C3(.2)^3(.8)^1+ 4C4(.2)^4(.8)^0]. So: The probability of getting exactly two of the eight four-option questions is 0.31146240234375. The probability of getting at least three of the four five-option questions is 0.0272. Those two are clearly independent. The product of those probabilities is 0.00847177734375. BUT...the answer is suppose to be 0.2552 apparently. Any input?