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 405 47 344 452 395 Mild 51 Strong Column Total 44 109 153 1000 500 500 Let's use the following notation for the various events: W = washing oil off within 5 minutes, A = washing ol 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)

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It doesn’t show the last parts (e) P(N or M) Are the events N= no reaction and M= mild reaction mutually exclusive? Explain. Yes. P(N and M) = 0. Yes P(N or M) = 0. No. P(N or M) ≠ 0. No. P(N or 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). 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).
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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.
Reaction
Within 5 Minutes
After 5 Minutes
Row Total
None
405
47
452
Mild
51
344
395
Strong
Column Total
44
109
153
500
500
1000
Let's use the following notation for the various events: W =
Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.)
washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction.
(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.
O Yes. P(N and M) = 0.
US V O 2:12
hp
Transcribed Image Text:Online Locker. Virtu. E Untitled document -. G kji - Google Search Spanish 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 405 47 452 Mild 51 344 395 Strong Column Total 44 109 153 500 500 1000 Let's use the following notation for the various events: W = Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.) washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. (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. O Yes. P(N and M) = 0. US V O 2:12 hp
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Probability is a numerical measure of the chance of occurrence of an event. In practice, we express the probability in terms of proportion or numbers.

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