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 allergi 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 summarize following table. Reaction None Mild Strong Column Total P(M) P(S) Within 5 Minutes After 5 Minutes 420 55 25 500 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 f sample of 1000 subjects. (Use 3 decimal places.) (a) P(N) (b) P(NIW) P(SW) (c) P(NIA) P(SA) (d) P(N and W) P(M and W) Row Total 460 403 137 1000 40 348 112 500

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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.
Within 5 Minutes
420
55
25
500
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)
Reaction
None
Mild
Strong
Column Total
(b) P(N | W)
P(S | W)
(c) P(NA)
P(S | A)
(d) P(Na W)
P(M and W)
After 5 Minutes
40
348
112
500
(e) P(N or M).
Row Total
460
403
137
1000
Are the events N = no reaction and M = mild reaction mutually exclusive? Explain.
O No. P(N and M) = 0.
O Yes. P(N or M) = 0.
O No. P(N or M) * 0.
O Yes. P(N and M) = 0.
(f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain.
O No. P(N and W) = P(N) P(W).
O Yes. P(N and W) P(N) P(W).
O Yes. P(N and W) = P(N) P(W).
O No. P(N and W) P(N) P(W).
Transcribed Image Text: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. Within 5 Minutes 420 55 25 500 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) Reaction None Mild Strong Column Total (b) P(N | W) P(S | W) (c) P(NA) P(S | A) (d) P(Na W) P(M and W) After 5 Minutes 40 348 112 500 (e) P(N or M). Row Total 460 403 137 1000 Are the events N = no reaction and M = mild reaction mutually exclusive? Explain. O No. P(N and M) = 0. O Yes. P(N or M) = 0. O No. P(N or M) * 0. O Yes. P(N and M) = 0. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. O No. P(N and W) = P(N) P(W). O Yes. P(N and W) P(N) P(W). O Yes. P(N and W) = P(N) P(W). O No. P(N and W) P(N) P(W).
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