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 NoneMildStrong 3916445 56336108 447400153 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. Yes. P(N and M) = 0.Yes. P(N or M) = 0. No. P(N and 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. No. P(N and W) = P(N) · P(W).Yes. 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).

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	391 64 45	56 336 108	447 400 153
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.

Yes. P(N and M) = 0.Yes. P(N or M) = 0. No. P(N and 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.

No. P(N and W) = P(N) · P(W).Yes. 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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