# llergic reactions to poison ivy can be miserable

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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*).