Survey: Reaction to Poison Ivy 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...

Survey: Reaction to Poison Ivy 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 Table 5-5.

Let’s use the following notation for the various events: W = washing oil off within 5 minute. 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.

(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) . Are the events N = no reaction and M = mild reaction mutually exclusive? Explain.
(f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain.

Extracted text: Time Within Which Oil Was Washed TABLE 5-5 off Row Reaction Within 5 Minutes After 5 Minutes Total None 420 50 470 Mild |60 330 390 Strong 20 120 140 Column Total 500 500 1000