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 utes 0 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. washed off after 5 minutes. The results are summarized in the following table. time left... 2:29:42 Within 5 Minutes After 5 Minutes Row Total None 413 42 455 Mild 51 344 395 Strong 36 114 150 Column Total 500 500 1000 Let's use the following notation for the various events: W = washing oil off within 5 minutes, A = washing oil off alter 5 minutes, N = no reaction, M = mild reaction, 5 = 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) ([7) PM W) P(S W) (C) PM A) P(S A) (d) P(N and W) P(M and W) (e) PM or M). Are the events N = no reaction and M = mild reaction mutually exclusive? Explain. 0 Yes. P(N orM) = 0. 0 Yes. PM and M) = O. O No. PM and M) at 0. O No. P(N orM) 0. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. 0 Yes. P(N and VII) = P(N) - P(W). O No. P(N and W) e P(N) - p(w)_ 0 Yes. PM and W) e P(N) . P(w)_ O No. P(Nand W) = pm) . P(W)- Submit