The probabilities of a boy passing English and Mathematics test are x and y respectively. Find the probability of the boy failing both tests

A.
1(xy)+xy 
B.
1(x+y)xy 
C.
1(x+y)+xy 
D.
1 – (x – y) + x
Correct Answer: Option C
Explanation
Prob (passing English) = x
Prob (passing Maths) = Y
Prob (failing English) = 1 – x
Prob (failing Maths) = 1 – y
Prob (failing both test) = Prob(failing English) and Prob(failing Maths) = (1 – x)(1 – y)
=1 – y – x + xy
=1 – (y + x) + xy