Allergic reaction to poison ivy can be miserable. plant oils cause the reaction

Question

Allergic reaction to poison ivy can be miserable. plant oils cause the reaction Researches at the 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 plait 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 i n the following table. 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. P(N), P(M), P(S) P(N|W), P(S|W) P(N|A), P(S|A) P(N and W), P(M and W) P(N or M)

Explanation / Answer

a)
P(N) = 470/1000 = 0.47

P(M) = 390/1000 = 0.39

P(S) = 140/1000   = 0.14

b)

P(N/W) = 420/500 = 0.84

P(S/W) = 20/500 = 0.04

c)
P(N/A) = 50/500 = 0.1

P(S/A) = 120/500 = 0.24

d)

P(N and W) = 420/1000 = 0.42

P(M and W) = 60/1000 = 0.06

e)

P(N or M) = (470+390)/1000 = 0.86

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