Allergic reactions to poison ivy can be miserable plant

Question

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 offwithin5 minutes. For the other 500 subjects, the oil was washed offafter5 minutes. The results are summarized in the following table.

Reaction	Within 5 Minutes	After 5 Minutes	Row Total
None Mild Strong	406 65 29	58 345 97	464 410 126
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.No. 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).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).