Allergic reaction to poison ivy can be miserable plant oils

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)

Solution

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