Question

Vehicles on a road can be classified into three categories according to their weight- Light, Medium. and
Heavy – with respective percentages 20%, 50%, 30%. Chances that they cause accidents. ore respectively 10%, 5% and
15%. Given that there is an accident, what is the probability that it was caused by a Heavy vehicle?

Answer 1

Let Light vehicle be L, Medium be M and Heavy be H .

Accident = A

P(L) = 0.20 , P(M) = 0.50 , P(H) = 0.30

P(A | L) = 0.10 , P(A | M) = 0.05, P(A | H) = 0.15

Using Bayes theorem,

P(H | A) = [ P(A | H) * P(H) ] / [  P(A | L) * P(L) +  P(A | M) * P(M) +  P(A | H) * P(H) ]

= [ 0.30 * 0.15 ] / [ 0.20 * 0.10 + 0.50 * 0.05 + 0.30 * 0.15 ]

= 0.50