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 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	Row Total
None Mild Strong	407 51 42	54 332 114	461 383 156
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)	0.461
	P(M)	0.383
	P(S)	0.156

(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).
0.844

Are the events N = no reaction and M = mild reaction mutually exclusive? Explain.

Yes. P(N or M) = 0.

No. P(N and M) ≠ 0.     

No. 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).

Answer 1