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 390 59 51 61 346 93 451 405 144 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.)

P(N)

P(M)

P(S)

P(N | W)

P(S | W)

P(N | A)

P(S | A) (d)

P(N and W)

P(M and W)

P(N or M).

Answer 1

please check below table if this is correct; as that given in question is not uploaded properly:

	<5 minute	> 5 minute	total
none	390	61	451
mild	59	346	405
strong	51	93	144
column total	500	500	1000

P(N)=451/1000=0.451

P(M)=405/1000=0.405

P(S)=144/1000=0.144

P(N|W)=390/500=0.78

P(S|W)=51/500=0.102

P(N|A)=61/500=0.122

P(S|A)=0.186

P(N and W)=390/1000=0.39

P( M and W) =59/1000=0.59

P(N or W)=(500+451-390)/1000=561/1000=0.561