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.

[Q]: 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
[A]: c


[Q]: Problem: last year elaine spent 20 % of her annual earnings on rent. this year she earned 35 % more than last year and she spent 30 % of her annual earnings on rent. the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a. 202.5, b. 194.5, c. 197.5, d. 182.5, e. 177.5
[A]: a


[Q]: Problem: given that x and y are events such that z ( x ) = 0.02 z ( y ) = 0.10 z ( xny ) = 0.10 z ( x | y ) = find z ( x | y ) and z ( x | y )
Options: a. 1 / 5, b. 1 / 6, c. 1 / 6, d. 1 / 4, e. 1 / 2
[A]:
a