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 409 55 36 43 348 109 452 403 145 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) Correct: Your answer is correct. P(M) Incorrect: Your answer is incorrect. P(S) Incorrect: Your answer is incorrect. (b) P(N | W) Incorrect: Your answer is incorrect. P(S | W) Incorrect: Your answer is incorrect. (c) P(N | A) Incorrect: Your answer is incorrect. P(S | A) Incorrect: Your answer is incorrect. (d) P(N and W) Incorrect: Your answer is incorrect. P(M and W) Incorrect: Your answer is incorrect. (e) P(N or M). Incorrect: Your answer is incorrect.

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	409	43	452
mild	55	348	403
strong	36	109	145
column total	500	500	1000

P(N)   =  452/1000

=0.452

P(M) = 403/1000

=0.403

P(S) = 145/1000

=0.145

P(N|W) = 409/500

=0.818

P(S|W) = 36/500

=0.072

P(N|A) = 43/500

=0.086

P(S|A) = 0.186

P(N and W) =409/1000

=0.409

P( M and W) = 55/1000

=0.055

P(N or W )= (500+452-409)/1000

=543/1000

=0.543