Solution: Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at allergy institute did a study to see the effects


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

  1. P(N), P(M), P(S)
  2. P(N|W), P(S|W)
  3. P(N|A), P(S|A)
  4. P(N, and W), P(M and W)
  5. P(N or M), are the events N=no reaction and M=mild reaction, mutually exclusive? Explain
  6. are the events N=no reaction and W=washing oil off within 5 minutes independent? Explain

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