1. Dene the following events for a randomly selected person from the population: 9 Ce 2 the person has COVID o Sp 2 the person shows COVID symptoms 0 T+ = the person tests positive for COVID You are also given the following probabilities for a randomly selected person: 0 The probability they have COVID is 500. o The probability1 they show symptoms given that they have COVID is 75%. I The probability1 they show symptoms given that they DON'T have COVID is 107;. o The probability1 they test positive given that they have COVID is 80% o The probability1 they test positive given that they have COVID AND show symp- toms is 98% o The probability1 they test positive given that they DON'T have COVID is 5% I The probability1 they test positive given that they DON'T have COVID AND they show symptoms is 10% Answer the following questions. calculating any probabilities in decimal form to at. least 5 decimal places: (a) (2 points} Express the above probabilities in terms of the events dened above. (Eg, the probability that a person has COVID is expressed as PiC'U) = 115.) (b) (2 points} Find the probability that a person shows symptoms. (0.} (3 points} Find the probability1 that a person has COVID. given that they show symptoms. ((1) (3 points} Find the prolmbilityl that a person tests positive, given that they have CUVID AND they DON'T show symptoms. (e) (4 points} Find the probabilityl that a person has COVID. given that they show symptoms AND being tested positive