(b) The reliability of a new rapid antigen test (A) and a new PCR test (P) are each to be assessed in a particular community affected by the SARS-CoV-2 virus. 55% of people in this community are virus-free, 20% have a low viral load, and the rest have a high viral load, respectively (this viral status (V) is recorded definitively via other means). Either test ( A or P) can yield a negative, inconclusive or positive result (i.e. 3 possible results), respectively. A statistical study provides the following conditional probability matrix estimates, relating viral load to the results of A and P, respectively: 0.75 0.23 0.02 0.93 0.10 0.01 TVA= 0.13 0.32 0.14 Typ = 0.07 0.11 0.01 0.12 0.45 0.84 0.00 0.79 0.98 Using this evidence, and stating any assumptions that you make, compute the following: (i) The probability that the results of A and P differ for a member of this community. [35 %] (ii) The probability that a member of this community is not virus-free, in the case evaluated in (i) (i.e. when the results of A and P differ). [20 %]