Question

Please answer Question 3 & show all work thanks

Due to mandated social isolation, you are alone in your apartment. The same is true about your significant other (S). Let's be honest, social isolation sucks! You are alone and lonely. You want to break the rules and visit S. Although your results were negative, you have no idea if S has covid-19. You figure that, S is healthy, eats well, works-out, and went in isolation early. So, you estimate the chances that S has covid-19 are 20% If S has covid-19, S is unlikely to open the door for you (10%). However, if S is free of covid-19, the likelihood of opening the door for you is 80% (not a 100% because you are still breaking the rules!). a. What is the Prob that has covid-19 but opens the door for you? b. What is the Prob that is free from covid-19 and opens the door for you? C. What is the Prob that S opens the door for you? d. Suppose s opens the door for you, what is the probability that S has covid-19?

Answer 1

a. probability that S has covid 19=20%

the probability that S will open the door when she has covid=10%

hence probability that S has covid-19 but opens the door=20%x10%=2%

b. probability that s is free from covid19=80%

the probability that S will open the door in this cse=80%

hence prob that S is free from covid and opens the door=80%x80%=64%

c. the probability that S opens the door= probability that S has covid-19 but opens the door+prob that S is free from covid and opens the door=64%+2%=66%

d. probabilty of { s having covid| S open the door }

=(probability of s having covid)(probability that she opens the door when she has covid)/{(probability that s has covid)(probability that she opens the door when she has covid)+probability that she doesn't have covid)(probability of she opening the door when she doesn't have covid)

=2%/2%+64%

=1/33

(refer to baye's theorem for part d)

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