Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 47

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 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reactions, 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.