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.                      402.      63. 465
Mild.                          67. 321.                       388
Strong.                       31. 116.                        147
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)    = .465
P(M)    .388
P(S)    .147

(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). =

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