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 offwithin 5 minutes. For the other 500 subjects, the oil was washed offafter 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 eventsN = no reaction andM = 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 eventsN = no reaction andW = 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).

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...

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 offwithin 5 minutes. For the other 500 subjects, the oil was washed offafter 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 eventsN = no reaction andM = 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 eventsN = no reaction andW = 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).

Jun 08, 2022

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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...

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