an exam consists of 8 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 80 % is a passing grade , what is the probability that brian passes ?
"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 125 / 256 . e"
add(divide(subtract(const_1, add(add(power(divide(const_1, const_2), 8), multiply(8, power(divide(const_1, const_2), 8))), multiply(multiply(8, const_3), power(divide(const_1, const_2), 8)))), const_10), subtract(const_1, add(add(power(divide(const_1, const_2), 8), multiply(8, power(divide(const_1, const_2), 8))), multiply(multiply(8, const_3), power(divide(const_1, const_2), 8)))))