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# Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction.

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 RowTotal

None 418 69 487

Mild 56 328 384

Strong 26 103 129

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 or M) = 0.

Yes. 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).

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).

(a) P(N) = (418 +69 )/1000 =0.487... View the full answer

• I have another question that needs help to please!
• donnaalversonfaulkner1
• Jun 06, 2018 at 10:01pm
• yes... You can post in course hero ...but not in comments please..as per honor policies
• SravyaVidya
• Jun 06, 2018 at 10:08pm
• yes it is posted, twice
• donnaalversonfaulkner1
• Jun 06, 2018 at 10:10pm

a.) P(N) = 0.487 P ( M ) = 0.384 P(S) =0.129 b.) P ( N  |  W ) = 0.836 P(S/W)... View the full answer

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