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sal minella came down with a nasty case of food poisoning. after researching his condition, he...

sal minella came down with a nasty case of food poisoning. after researching his condition, he found that 40% of patients don’t go to the doctor, 35% of patients go to the doctor and 25% of patients go to the emergency room. respectively, 30%, 50% and 70% of patients feel better within 24 hours.
a) find the probability that a ramdomly selected patient feels better after 24 hrs.
b) a patient feels better. find the probability that they went to the doctor.
c) find the probability that if a patient doesn't feel better, they went to the emergency room.
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Answer #1

a)P(feels better)=P(don't go to doctor)*P(feels better|don't go to doctor)+P(go to doctor)*P(feels better|go to doctor)+P(emergency)*P(feels better|emergency)

=0.4*0.3+0.35*.5+0.25*0.7=0.47

b)

P(go to doctor |feels better)=P(go to doctor)*P(feels better|go to doctor)/P(feels better)

=0.35*0.5/0.47 =0.3723

c)

P(P(emergency |do not feel better)

=P(emergency)*P(do not feels better|emergency)/P(do not feels better)

=0.25*0.7/(1-0.47)=0.3302

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