In this task, you need to provide the correct option for a given problem from the provided options.

[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 0.20 . the probability that neither a nor b occur is _________ 
Options: a ) 0.45 , b ) 0.4 , c ) 0.55 , d ) 0.05 , e ) 0.6
[A]: c


[Q]: Problem: a certain hobby shop sold model cars for $ 5.00 each and model trains for $ 8.00 each . if a customer purchased both cars and trains from the store for a total of $ 31.00 , what total number of cars and trains did the customer purchase ? 
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
[A]: c


[Q]: Problem: at the faculty of aerospace engineering , 312 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ? 
Options: a ) 424 . , b ) 428 . , c ) 430 . , d ) 432 . , e ) 436
[A]:
d