Survey: Reaction to Poison Ivy Allergic reactions to poison ivy can bemiserable. Plant oils cause the reaction. Researchers at Allergy Institutedid a study to determine the effects of washing the oil off within 5minutes of exposure. A random sample of 1000 people with knownallergies to poison ivy participated in the study. Oil from the poison ivyplant 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 waswashed off after 5 minutes. The results are summarized in Table 5-5. TABLE 5-5 Time Within Which Oil Was Washed off Reaction Within 5 Minutes after 5 Minutes Row Total NoneMildStrongColumn Total 4206020500 50330120500 4703901401000 Let's use the following notation for the various events: W= washing oiloff within 5 minute. A = washing oil off after 5 minutes. N= no reaction. M= mild reaction. S= strong reaction. Find the following probabilitiesfor a person selected at random from this sample of 1000 subjects. (a) P (N), P(M), P (S)(b) P(N| W), P(S | W)(c) P(N | A). P(S |4)(d) P(N and W). P (M and W) (e) P (N or M). Are the events N= no reaction and M= mild reactionmutually exclusive? Explain.(f) Are the events N =no reaction and W=washing oil off within 5minutes independent? Explain.
Survey: Reaction to Poison Ivy 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 Table 5-5.
| TABLE 5-5 | Time Within Which Oil Was Washed off | ||
| Reaction | Within 5 Minutes | after 5 Minutes | Row Total |
| None Mild Strong Column Total |
420 60 20 500 |
50 330 120 500 |
470 390 140 1000 |
Let's use the following notation for the various
off within 5 minute. 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.
(a) P (N), P(M), P (S)
(b) P(N| W), P(S | W)
(c) P(N | A). P(S |4)
(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.
(f) Are the events N =no reaction and W=washing oil off within 5
minutes independent? Explain.
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