Question Hypothetical In a particular city there are three

Question : (Hypothetical) In a particular city, there are three hospitals, we label them as N (as in North), E (as in East) and S (as in South) hospitals. During normal operations, 30% of persons are admitted to the North hospital, 20% to the East hospital and 50% admitted to the South hospital (perhaps from a facility downtown). Unfortunately, a certain illness (we label it here as F as in ‘flu’) appears to be spreading amongst these three hospitals with the infection rates at the various hospitals given by 20% for the North, 30% for the East and 50% for the South hospital. Suppose that one person is selected from the outpatients form all three hospital in a totally random fashion. Find the probability that this person

(Hint: use the Array technique with headings N, E and S etc show it here….

a) Is from North-hospital and contacted the illness there

b) Has contacted the illness (from any of the hospitals)

c) Is from the South hospital given s/he had the illness

d) Are the two events in part c) independent or dependent (give reasoning

Solution

A) 30% GO IN NORTH AND INFECTION IN NORTH IS 20%

SO THE CHANCES OF BEING AFFECTED FROM NORTH IS 0.2*0.3 = 0.06

B) CHANCES FROM NORTH WILL BE 0.06 AS SOLVED ABOVE

CHANCES FROM SOUTH WILL BE 0.5*0.5 = 0.25( AS 50% PATIENTS ARE THERE AND 50% INFECTION IS THERE.

CHANCES OF BEING AFFECTED FROM EAST = 0.2*0.3 = 0.06

SO ADD ALL 0.06+0.25+0.06 = 0.37

C) GIVEN THAT THERE IS AN ILL PATIENTS THEN THE PROBABILITY OF HIM BEING FROM SOUTH WILL BE 50% AS GIVEN IN THE QUESTION = 0.5

D) ITS INDEPENDENT BECAUSE A PERSON CAN FALL AFFECTED OUTSIDE THE SOUTH ALSO, BEING AFFECTED IS NOT DEPENDENT ON BEING ONLY FROM SOUTH

HENCE INDEPENDENT