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.
























ReactionWithin 5 MinutesAfter 5 MinutesRow Total
None
Mild
Strong
391
69
40
59
326
115
450
395
155
Column Total5005001000


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.
No.P(N and M) ≠ 0.

Yes.P(N and M) = 0.

 No.P(N or M) ≠ 0.

Yes.P(N or M) = 0.


(f) Are the eventsN = no reaction andW = washing oil off within 5 minutes independent? Explain.
Yes.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).

No.P(N and W) ≠P(N) ·P(W).

Jun 01, 2022
SOLUTION.PDF

Get Answer To This Question

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here