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.ReactionWithin 5 MinutesAfter 5 MinutesRow TotalNoneMildStrong396535152343105448396156Column Total5005001000Let'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 or M) ≠ 0.No. P(N and 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).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).

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 13CYU

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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	396 53 51	52 343 105	448 396 156
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.)

(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 or M) ≠ 0.No. P(N and 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).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).

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