Question

1. DETAILS 75% of positively tested Cavid-18 cases and 10% of negatively tested Cavid 19 cases are showing ptoms. Given that 25% of the Covid 19 tests are positive. Find the following round up to 4 de points) Finding the pretty that a randomly tested on the Cold 19 tome boven that a random persons whowing Cevid 10 toms, what is the pray that a Cavid-19 let for that person is positive 6. Given that a random person is not showing any Cov-19 symptom, what is the probly that a Cavid-19 test for that person is positive

75% of positively tested covid 19 cases and 10% of negatively are showing symptons. given that 25% of the tests are positive find the following:

1)probability that a randomly tested person is showing symptons

2)given that a random person is showing symptons what is the prob that a covid test for that person is positive?

3) given that a person is not showing symptons, what is the prob that a covid test for that person is positive?

Answer 1

- Let the event et and a represent the scenario a person to test positive and regative respectively. Then P(t) = 0.25, P(-) = 1- P(+) = 0.75 that Let yes' and 'No? be the event the person and doesn't show syimptoms respectively, shows So, P(yes)t) = 0.75 and Plyes 1-) = 0.1 Thus, probability that randomly tested person Sheeting symptoms in Plyes) = P(t). Plyes(+) + P(-). P(yes 1-) (0.25)(0.75) + (0.75) (0.1) 0.1875+ 0.075 - 0.2625 2) This is the conditional probability P(+1yes). P(+ nyes) P(+). Plyes(+) So, P(+1yes) = Plyes) Plyes) 10.25) 10.75) 0.1875 10.71431 0.2625 0.2625 which gives This į because :- P(A/B) = P(ANB) P(B) P(BIA) = P(BNA) = P(AIB) xP (B) PCA) PCA)

83) P(No)= P(+) - P(Nolt) + P(-) . P(No1-) (0.25) (0.25) + (0.75) (0.9) 0.0625 + 0.675 so 0.7375 the conditional probability P(+1No) is : p(+1No) = P(Anno) P(+). Plnol +) P (NO) PINO) (0.25)(0.25) 0.7375 ñ 10.0847