Recitation 18 Problem 1. There is a rare and deadly disease called nerditosis which afflicts about 1 per son in 1000. On symption is a compulsion to refer to everything- fields of study, classes, buildings, etc- using numbers. It's horrible. As victims enter their final, downward spiral, theyre awarded a degree from MIT. Two doctors claim that they can diagnose Nerditosis (a) Doctor X received his degree from Harvard Medical School. He practices at Mas- sachusetts General Hospital and has access to the latest scanners, lab tests, and re- search. Suppose you ask Doctor X whether you have the disease If you have Nerditosis, he says"yes"with probability 0.99 If you dont have it, he says"no"with probability 0.97 Let d be the event that you have the disease, and let e be the event that the diag- nosis is erroneous. Use the Total Probability Law to compute Pr(E), the probability that Doctor X makes a mistake Solution. By the Total Probability Law Pr(E)=Pr(EI D). Pr(D)+Pr(EID). Pr(D =0.01.0.001+0.03·0.999 (b)" Doctor"Y received his genuine degree from a fully-accredited university for $49.95 via a special internet offer. He knows that Nerditosis stikes 1 person in 1000, but is a little shakey on how to interpret this. So if you ask him whether you have the disease, he'll helpfully say"yes" with probability 1 in 1000 regardless of whether you actually do or not Let d be the event that you have the disease, and let F be the event that the diag nosis is faulty. Use the Total Probability Law to compute Pr(F), the probability that Doctor y made a mistake Solution by the Total Probability Law Pr(F)=Pr(FI D). Pr(D)+Pr(FID). PrD 0.999·0.001+0.001.0.999 0.001998 (c) Which doctor is more reliable? Solution. Doctor X makes more than 15 times as many errors as doctor y� � � � � � � � Recitation 18 2 Problem 1. There is a rare and deadly disease called Nerditosis which afflicts about 1 per￾son in 1000. On symption is a compulsion to refer to everything— fields of study, classes, buildings, etc.— using numbers. It’s horrible. As victims enter their final, downward spiral, they’re awarded a degree from MIT. Two doctors claim that they can diagnose Nerditosis. (a) Doctor X received his degree from Harvard Medical School. He practices at Mas￾sachusetts General Hospital and has access to the latest scanners, lab tests, and re￾search. Suppose you ask Doctor X whether you have the disease. • If you have Nerditosis, he says “yes” with probability 0.99. • If you don’t have it, he says “no” with probability 0.97. Let D be the event that you have the disease, and let E be the event that the diag￾nosis is erroneous. Use the Total Probability Law to compute Pr (E), the probability that Doctor X makes a mistake. Solution. By the Total Probability Law: Pr (E) = Pr (E | D) · Pr (D) + Pr E D | · Pr D = 0.01 · 0.001 + 0.03 · 0.999 = 0.02998 (b) “Doctor” Y received his genuine degree from a fully­accredited university for $49.95 via a special internet offer. He knows that Nerditosis stikes 1 person in 1000, but is a little shakey on how to interpret this. So if you ask him whether you have the disease, he’ll helpfully say “yes” with probability 1 in 1000 regardless of whether you actually do or not. Let D be the event that you have the disease, and let F be the event that the diag￾nosis is faulty. Use the Total Probability Law to compute Pr (F), the probability that Doctor Y made a mistake. Solution. By the Total Probability Law: Pr (F) = Pr (F D| ) · Pr (D) + Pr F | D · Pr D = 0.999 · 0.001 + 0.001 · 0.999 = 0.001998 (c) Which doctor is more reliable? Solution. Doctor X makes more than 15 times as many errors as Doctor Y