The probability that a one-car accident is due to faulty brakes is $0.04$, the probability that a one-car accident is correctly attributed to faulty brakes is $0.82$, and the probability that a one-car accident is incorrectly attributed to faulty brakes is $0.03$. What is the probability that
$(a)$ a one-car accident will be attributed to faulty brakes;
$(b)$ a one-car accident attributed to faulty brakes was actually due to faulty brakes?
Is my interpretation of this problem correct? If so can I continue and use the Rule of total probability and conditional probability?
$B_{1} = \{ \text{Car accident due to faulty brakes \}}$
$B_{2} = \{ \text{Car accident NOT due to faulty brakes \}}$ (refers to elements not in $B_{1}$)
$P = \{ \text{attributed to brakes}\}$
$N = \{ \text{NOT attributed to brakes}\}$
$P(B_{1}) = .04 \; \; \;P( B_{2})= .96$
$P(P|B_{1}) = .82$
$P(P|B_{2}) = .03 $
$P(N|B_{1}) = 1-.82 =.18$
$P(N|B_{2}) = 1-.03 = .97 $