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12) Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers 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 plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in Table 5-5. Time within which oil was washed off
Reaction within 5 minutes After 5 minutes Row total
None 420 50 470
Mild 60 330 390
Strong 20 120 140
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= 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) P (N or M). 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.

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