Question 995564: please help me work out this question. was given to me as an assignment by my tutor but i have failed to work it out.
Taonga has contracted a virus V which can be of type V1,V2,V3.The probability of the virus being V1,V2,V3 is 0.3,0.6,0.1 respectively .The probability of recovery for V1,V2,V3 is 0.8,0.3,0.5 respectively .what is the probability that
(a) Taonga recovers
(b) If Taonga recovers then she had V2?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! "The probability of the virus being V1,V2,V3 is 0.3,0.6,0.1 respectively" means that
 of the patients with virus V have type V1;
 of the patients with virus V have type V2, and
 of the patients with virus V have type V3.
Out every 100 patients with virus V,
30 will have V1, 60 will have V2, and 10 will have V3.
Of the 30 patients with V1,  will recover.
That amounts to  patients with V1 recovering.
Of the 60 patients with V2,  will recover.
That amounts to  patients with V2 recovering.
Of the 10 patients with V3,  will recover.
That amounts to  patients with V3 recovering.
All in all, out of the  patients with virus V,
 recover.
The fraction of the patients that recover is  ,
and that is the probability that Taonga recovers:  .
Of each set of 100 patients,  recover,
and of those ,
 had V2, amounting to  of those who recovered.
That is the probability that if Taonga recovers Taonga had V2:
 = about = about .
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