- For mathematical modeling, suppose the major causes of an accident (A) on a se

Question

- For mathematical modeling, suppose the major causes of an accident (A) on a segment of
highway can be grouped into speeding (S), tiredness (T), carelessness (C), weather conditions
(W), and drunkenness (D). likelihood of these causes is estimated to be 4:3:1:1:1,
respectively. The probabilities of an accident due to S, T, C, W, and D are 0.01, 0.05, 0.01,
0.005, and 0.8, respectively.
Calculate the probability of an accident in the segment of a highway.
If there was an accident, what is the probability that it was caused by drunkenness of the
driver?

Explanation / Answer

For mathematical modeling, suppose the major causes of an accident (A) on a segment of
highway can be grouped into speeding (S), tiredness (T), carelessness (C), weather conditions
(W), and drunkenness (D). likelihood of these causes is estimated to be 4:3:1:1:1,
respectively. The probabilities of an accident due to S, T, C, W, and D are 0.01, 0.05, 0.01,
0.005, and 0.8, respectively.
Calculate the probability of an accident in the segment of a highway.
If there was an accident, what is the probability that it was caused by drunkenness of the
driver?

from the given likelihood,

P(S) =0.4       P(T)=0.3     P(C) =0.1      P(W) =0.1    P(D) =0.1

P(A/S) =0.01     P(A/T)=0.05    P(A/C) =0.01     P(A/W) =0.005    P(A/D) =0.8

Bayes’ theorem used

Probability of an accident in the segment of a highway

P(A) = P(A/S)* P(S)+ P(A/T)* P(T)* P(A/C)* P(C)+ P(A/W)* P(W)+ P(A/D)* P(D)

=0.01*0.4+0.05*0.3+0.01*0.1+0.005*0.1+0.8*0.1

=0.1005

If there was an accident, what is the probability that it was caused by drunkenness of the
driver?

P( D/A) = {P(A/D)* P(D) } / P( A)

=(0.8*0.1)/0.1005

=0.796

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