Survey: Reaction to Poison Ivy Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in Table 4-6.

TABLE 4-6 Time Within Which Oil Was Washed Off Reaction Within 5 Minutes After 5 Minutes Row Total None 420 50 470 Mild 60 330 390 Strong 20 120 140 Column Total 500 500 1000 Let’s use the following notation for the various events:
W 5 washing oil off within 5 minutes, A 5 washing oil off after 5 minutes, N 5 no reaction, M 5 mild reaction, S 5 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(N | W), P(S | W)

(c) P(N | A), P(S | A)

(d) P(N and W), P(M and W)

(e) P(N or M). Are the events N 5no reaction and M 5mild reaction mutually exclusive? Explain.

(f) Are the events N 5 no reaction and W 5 washing oil off within 5 minutes independent? Explain.AppendixLO1