Question

Question

llergic 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 Minutes After 5 Minute Row Total none

none 408 47 455

mild 62 333 395

Strong 30 120 150

Column Total 500 500 1,000

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.

No. P(N or M) ≠ 0.

Yes. P(N or M) = 0.

Yes. P(N and M) = 0.

(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).

Yes. P(N and W) = P(N) · P(W).

No. P(N and W) ≠ P(N) · P(W).

No. P(N and W) = P(N) · P(W).

llergic 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 Minutes After 5 Minute Row Total none

none 408 47 455

mild 62 333 395

Strong 30 120 150

Column Total 500 500 1,000

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.

No. P(N or M) ≠ 0.

Yes. P(N or M) = 0.

Yes. P(N and M) = 0.

(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).

Yes. P(N and W) = P(N) · P(W).

No. P(N and W) ≠ P(N) · P(W).

No. P(N and W) = P(N) · P(W).

 

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