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. Reaction Within 5 Minutes After 5 Minutes Row Total None Mild Strong 409 55 36 52 326 122 461 381 158 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. (Use 3 decimal places.) (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. No. P(N and M) ≠ 0. Yes. P(N and M) = 0. Yes. P(N or M) = 0. No. P(N or M) ≠ 0. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. Yes. P(N and W) = P(N) · P(W). No. P(N and W) = P(N) · P(W). No. P(N and W) ≠ P(N) · P(W). Yes. P(N and W) ≠ P(N) · P(W).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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. Reaction Within 5 Minutes After 5 Minutes Row Total None Mild Strong 409 55 36 52 326 122 461 381 158 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. (Use 3 decimal places.) (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. No. P(N and M) ≠ 0. Yes. P(N and M) = 0. Yes. P(N or M) = 0. No. P(N or M) ≠ 0. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. Yes. P(N and W) = P(N) · P(W). No. P(N and W) = P(N) · P(W). No. P(N and W) ≠ P(N) · P(W). Yes. P(N and W) ≠ P(N) · P(W).

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