crime is committed by one of two suspects, A and B$.$ Initially, there is equal evidence against

both of them. In further investigation at the crime scene, it is found that the guilty party had a

blood type found in $10\%$ of the population. Suspect A does match this blood type, whereas the

blood type of Suspect B is unknown.

$($a$)$ Given this new information, what is the probability that A is the guilty party? $($Hint:

P $($A matches the blood type $|$ A is the guilty party$)=1.)$

$($b$)$ Given this new information, what is the probability that B$$s blood type matches that found

at the crime scene