Answer
By using complement rule,
P(A^{c}|C) = 1 - P(A|C) = 1 - 0.9 = 0.1
P(B^{c}|C) = 1 - P(B|C) = 1 - 0.95 = 0.05
P(No system detects) = P(A^{c} ∩ B^{c}|C)
P(A^{c} ∩ B^{c}|C) = P(A^{c}|C) . P(B^{c}|C)
= 0.1 x 0.05 = 0.005
P(At least one system detects) = 1 - P(A^{c} ∩ B^{c}|C)
= 1 - 0.005 = 0.995
Work Step by Step
As given in answer
