Question: Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at allergy institute did a study to see the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy plant was rubbed a patch of skin. For 500 subjects, the oil was washed off after 5 minutes. The results are summarized in the following table.

Use the following notations for the various events

W=washing off oils in 5 minutes

A= washing off oils after 5 minutes

N=no reaction

M=mild reaction

S=strong reaction

(a) P(N), P(M), P(S)

(b) P(N, given W), P(S, given W)

(c) P(N, given A), P(S, given 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