TASK DEFINITION: Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.
PROBLEM: Problem: the probability of two events a and b are 0.25 and 0.40 respectively. the probability that both a and b occur is 0.15. the probability that neither a nor b occur is _________
Options: a. 0.45, b. 0.4, c. 0.5, d. 0.05, e. 0.6

SOLUTION: c

PROBLEM: Problem: students at a school were on average 180 cm tall. the average female height was 170 cm, and the average male height was 182 cms. what was the ratio of men to women ?
Options: a. 5: 2, b. 5: 1, c. 4: 3, d. 4: 1, e. 3: 1

SOLUTION: b

PROBLEM: Problem: a certain high school has 500 students. of these students, 30 are taking music, 10 are taking art, and 10 are taking both music and art. how many students are taking neither music nor art ?
Options: a. 430, b. 440, c. 450, d. 460, e. 470

SOLUTION:
e