Question

(c) How would you make a probability assignment to this s ample spu when you drop 500 tacks, 340 land flat side down? 12. Survey: Reaction to Poison Ivy Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy ins a study to determine the effects of titute did washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poiso ivy participated in the study. Oil from the poison ivy plant was ru patch of s the other 500 subjects, the oil was washed off after 5 minutes. summarized in Table 4-5 bbed on a Kin. For 500 of the subjects, it was washed off within 5 minutes. For The results are TABLE 4-5 Time Within Which Oil Was Washed Off Row Total 470 390 140 1000 Reaction None Within 5 Minutes 420 60 20 500 After 5 Minutes 50 330 120 500 Mild Strong Column Total Let's use the following notation for the various events: W = washing oil off within 5 minute, A washing oil off after 5 minutes, N-no reaction, M mild reaction, S strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects (a) P(N), P(M), P(s) (b) P(NI W), P(SI W) (c) P(NIA), P(SIA) (d) P(N and W), PM and W) (e) P(N or M). Are the events N no reaction and Mmild reaction mutu- ally exclusive? Explain. (f) Are the events N - no reaction and W washing oil off within 5 minutes independent? Explain.

Answer 1

Answer: ---- Date: ----15/5/2019

The distribution table for the given data is as follows Within 5 minAfter 5 min Row Total Reaction None Mild Stron Column Total 420 60 20 500 50 330 120 500 470 390 140 1000 390)0004 140 P(M)=390-E39] P(N)-470- ] 10.47 1000 1000 P(Nn) 420 =500-1084 P(W) P(SnA)120 NIA)= P( 0.24 -P(d)--500 = 420 1000 P(NOW0.42P(MW)-0.06 1000

0.47+0.39-0 -0.86 The events no reaction and mild reaction are mutually exclusive since, P(NM) 0 The events no reaction and washing oil off within 5 minutes are independent if and only P(NnW) 0.42 P(N)x P(W)0.47x0.5 0.235 Thus, the events no reaction and washing oil off within 5 minutes are not independent.