Reaction Within 5 Minutes After 5 Minutes Row Total None 406 65 471 Mild 57 344 401 Strong Column Total 37 91 128 500 500 1000
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 the following table.
Let's use the following notation for the various
| (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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