12. 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 4-5.

Let’s use the following notation for the various events: W 5 washing oil off within 5 minute, 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) P1N2, P1M2, P1S2

(b) P1N | W2, P1S | W2

(c) P1N | A2, P1S | A2

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

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

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

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TABLE 4-5 Time Within Which Oil Was Washed Off Reaction None Within 5 Minutes After 5 Minutes Row Total 420 50 470 Mild 60 330 390 Strong 20 120 140 Column Total 500 500 1000