Probability of solving one problem=85/100=0.85. Let p=0.85. The probability of failing to solve a problem is 1-p=0.15. Let q=0.15, then (p+q)4=1 represents all possible outcomes.
In words, these terms represent:
all questions correct
3 correct, 1 wrong
2 correct, 2 wrong
1 correct, 3 wrong
So exactly three correct is the second term 4p3q=4(0.85)3(0.15)=0.368 or 36.8% approx.