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 391 69 40 59 326 115 450 395 155 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 and W) P(M and W) (b) P(N or M). Are the events N = no reaction and M = 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. (c) 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)
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 391 69 40 59 326 115 450 395 155 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 and W) P(M and W) (b) P(N or M). Are the events N = no reaction and M = 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. (c) 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)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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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 |
391 69 40 |
59 326 115 |
450 395 155 |
| 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 and W) | ||
| P(M and W) |
(b) P(N or M).
Are the events N = no reaction and M = 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.
(c) 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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