\\; *Hi 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. Reaction Within 5 Minutes Aer 5 Minutes Row Total None 409 44 453 Mild 64 339 403 Strong 27 117 144 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 after 5 minutes, N 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 No. P(N and M) at 0. O No. P(N or M) 0. 0 Yes. P(N or M) = 0. 0 Yes. P(N and M) = o. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. O No. P(N and W) s P(N) - P(W). 0 Yes. P(N and W) = pm) . P(w)_ 0 Yes. P(N and W) e P(N) . P(w)_ O No. P(Nand W) = pm) . P(W)- = no reaction, M = mild reaction, 5 = strong reaction. Find the following probabilities for a