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-(x-y)+xy
B
1-(x+y)-xy
C
1-(x+y)+xy
D
1 - (x - y) + x
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #26606)