Steve guesses randomly on a 15-question multiple choice test in which each problem has two choices, a correct one and an incorrect one. What is the

well, the probability of him getting the first question right is 1/2, and the probability of him getting the first and second questions correct is 1/2*1/2 and so on. since there are 15 different questions and 15 is an odd number, at least halve of 15 is [15/2]=8. so that means we have to multiply 1/2 by 1/2 eight times but doing this could be a bit tedious, so we do (1/2)⁸=1/(2⁸)=1/256

so the probability of him getting at least halve the questions correct is 1/256

noooooooooooo that's wrong 

"At least half" means that he gets 8 or more correct.

Probability of getting 8 correct

C(15,8)(1/2)^8(1/2)^7  = 6435/32768

Probability of getting 9 correct

C(15,9)(1/2)^9(1/2)^6 =   5005/32768

Probability of getting 10 correct

C(15,10)(1/2)^10(1/2)^5 = 3003/32768

Probability of getting 11 correct

C(15,11)(1/2)^11(1/2)^4  = 1365/32768

Probability of getting 12 correct

C(15,12)(1/2)^12(1/2)^3 = 455/32768

Probability of getting 13 correct 

C(15,13)(1/2)^13(1/2)^2 = 105/32768

Probability of getting 14 correct

C(15,14)(1/2)^14(1/2)^1 = 15/32768

Probability of getting 15 correct =

C(15,15)(1/2)^15(1/2)^0  = 1/32768

So....the total probability is  =   [6425 + 5005 + 3003 + 1365 + 455 + 105 + 15 + 1 ] / 32768   =

16374/32768  = 8187/16384

Thanks to Alan for spotting my typo.....the correct answer should be....

  [6435 + 5005 + 3003 + 1365 + 455 + 105 + 15 + 1 ] / 32768   = 1/2   !!!!