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: 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
c

Problem: increasing the original price of a certain item by 25 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent ?
Options: a. 31.25, b. 37.5, c. 50.0, d. 52.5, e. 62.5
e

Problem: in an election, candidate a got 55 % of the total valid votes. if 15 % of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate ?
Options: a. 261800, b. 355800, c. 356500, d. 356800, e. 357000

a