Question 995564
"The probability of the virus being V1,V2,V3 is 0.3,0.6,0.1 respectively" means that
{{{0.3=30/100}}} of the patients with virus V have type V1;
{{{0.6=60/100}}} of the patients with virus V have type V2, and
{{{0.1=10/100}}} 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, {{{0.8=8/10=8/100="80%"}}} will recover.
That amounts to {{{30*0.8=24}}} patients with V1 recovering.
Of the 60 patients with V2, {{{0.3=3/10=30/100="30%"}}} will recover.
That amounts to {{{60*0.3=18}}} patients with V2 recovering.
Of the 10 patients with V3, {{{0.5=5/10=50/100="50%"}}} will recover.
That amounts to {{{10*0.5=5}}} patients with V3 recovering.
All in all, out of the {{{100}}} patients with virus V,
{{{24+18+5=47}}} recover.
The fraction of the {{{100}}} patients that recover is {{{47/100=0.47}}} ,
and that is the probability that Taonga recovers: {{{highlight(0.47)}}} .


Of each set of 100 patients, {{{47}}} recover,
and of those {{{47}}} ,
{{{18}}} had V2, amounting to {{{18/47}}} of those who recovered.
That is the probability that if Taonga recovers Taonga had V2:
{{{highlight(18/47)}}}= about{{{highlight(0.383)}}}= about{{{highlight("38.3%")}}} .