A small village, which has no hospital nearby, is served by three mobile units c

Question

A small village, which has no hospital nearby, is served by three mobile units coming from three centers A, B, and C. These units also serve many other villages in the region. The units pass through the village several times a day and they appear on the average frequently. What is the probability that a waiting patient will be served by the unit coming from center B? Now, suppose unit A can serve only adult males, unit B can serve adult females and children, but not adult males, and C can serve everyone. Furthermore, C makes half the number of trips to any village compared to A and B. What is the probability that a waiting adult male patient will be served by the first mobile unit arriving on the scene?

Explanation / Answer

a. there are equal chances that a waiting patient is served by any center A, B and C is 0.33

therefor a waiting patient is served by center B is 0.33

b. A waiting male patient can be served by either A or C

now C makes half of the trips hence the probability that a waiting patient served by C is 0.5

probability of a waiting patient is served by A is 0.25

but both the events are mutually exclusive

hence P( a adult waiting male is served) = P(A arrives) +P( C arrives) = 0.25+0.5 =0.75

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