Intersection A is located downstream of intersection B. A traffic engineer obser

Question

Intersection A is located downstream of intersection B. A traffic engineer observed that during the morning peak period the probability that intersection A is congested is 0.30. There is a 0.50 probability of A being congested given the knowledge that B is congested. On the other hand, the probability of B being congested given the knowledge that A is congested in 0.90. Calculate the probability that (a) B is congested during the peak period and (b) at least one of the two intersections is congested.

Explanation / Answer

Given,

P(A is congested) = 0.30

P(A is congested | B is congested) = 0.50

P(B is congested | A is congested) = 0.90

Hence,

a) P(A and B both are congested)

= P(A is congested | B is congested)*P(B is congested) = P(B is congested | A is congested)*P(A is congested)

So,

0.50*P(B is congested) = 0.90*0.30

P(B is congested) = 0.90*0.30/0.50 = 0.54

b) P(At least one of the two intersections is congested)

= P(A is congested) + P(B is congested) - P(Both are congested)

= 0.30 + 0.54 - 0.90*0.30

= 0.57

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