An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 60% is a passing grade, what is the probability that Brian passes?
Choose the correct choice
A) 1/16 B) 37/256 C) 1/2 D) 35/256 E) 15/16
If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.   If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.   So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.   Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.   The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 35/256.   35/256
<result>D</result>
An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 60% is a passing grade, what is the probability that Brian passes?