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 402 55 43 64 323 113 466 378 156 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.) (d) P(N and W) P(M and W) (e) P(N or M). (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). Yes. P(N and W) ≠ P(N) · P(W).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	402 55 43	64 323 113	466 378 156
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.)

(d)	P(N and W)
	P(M and W)

(e) P(N or M).

(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).

Yes. P(N and W) ≠ P(N) · P(W).

No. P(N and W) ≠ P(N) · P(W).

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