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...

Extracted text: 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 the following table. Row Total Reaction None Mild Within 5 Minutes After 5 Minutes 390 59 51 500 70 343 87 500 460 402 138 1000 Strong Column Total Let's use the following notation for the various events: W = washing oil off within 5 minutes, 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. (Use 3 decimal places.) (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 = no reaction and M = mild reaction mutually exclusive? Explain. O Yes. P(N or M) = 0. O No. P(N and M) + 0. O Yes. P(N and M) = 0. O No. P(N or M) + 0. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. O Yes. P(N and W) + P(N) · P(W). O Yes. P(N and W) = P(N) · P(W). O No. P(N and W) = P(N) · P(W). O No. P(N and W) + P(N) · P(W).