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 5-5.

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 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.