Answer:
a)  P[A/B] = 0,019     or     P[A/B] = 1,9 %
b)  P[A- /B-] = 0,9996       or    P[A- /B-] = 99,96 %
Step-by-step explanation:
Bayes Theorem :
P[A/B]  =  P(A) * P[B/A] / P(B)
The branches of events are as follows
Condition 1        real infection     1/300        and     not infection  299/300
Then
 1.-    1/300      299/300
When the test is done   (virus present)  0,9 (+)    0,15 (-)
2.-   299/300
When the test is done  ( no virus )   0,15  (+)     0,85 (-)
Then:
P(A) = event person infected          P(B)  =  person test positive
a) P[A/B]  = P(A) * P[B/A] / P(B)
where   P(A)  = 1/300  =   0,0033   P[B/A] = 0,9    
Then P(A) * P[B/A] =  0,0033*0,9  =  0,00297
P(B)   is    ( 1/300 )*0,9  +  (299/300)*0,15
P(B) = 0,0033*0,9 + 0,9966*0,15    ⇒  P(B) = 0,1524
Finally
P[A/B] =  0,00297 /0,1524
P[A/B] = 0,019     or     P[A/B] = 1,9 %
b) Following sames steps:
P[A- /B-] = (299/300) * 0,85  / (299/300) * 0,85 + (1/300 * 0,1)
P[A- /B-] = 0,8471 /0,8474
P[A- /B-] = 0,9996       or    P[A- /B-] = 99,96 %