(1)) W hat is the. total probability that an infected patient slums symptoms Within one day of infection? (i'e.= what is P(X 6 | {X > 3} 8)?) (3 pts) 1. Two equally prevalent viruses, virus A and virus 13,. have similar symptoms, but virus A is much more deadlyr than virus 13. If a patient is infected with virus A and is not treated, they is a high risk that patient will diej but the treatment for virus A is expensive: limited in supply: and will have no effect if given to a patient infected with virus 13, so it is important to be able to distinguish between the two viruses for diagnostic purposes to determine whether the treatment is appropriate. It has been determined that the best way to differentiate between the two viruses is their incubation period (the time between when a patient is infected and when they first present syinpton'ls); both virus have exponentially distributed incubation periods, but the mean incubation period for virus A is 3 days, while the mean incubation period for virus B is 6 days (denoting the nit-ulnation period for an infected patient by X, this means that X ~ Exp(1/3) if the patient is infected with virus A, and X ~ Epr/(i) if the patient is infected with virus B). NOTE: Letting A : {infected patient has virus A} and B : {infected patient has virus B}, assume PUD : 13(3) 2 1X2 for an infected patient since both viruses are equally prevalent