Researchers sampled 1971 German men to determine if there is

Researchers sampled 1971 German men to determine if there is a relationship between their eye and hair colors. The cross-tabulated results of their sample are given in the contingency table below.

Suppose you randomly select a German man. Find each of the following probabilities.
Note: You can answer as a fraction or in decimal form. Round to 4 decimal places if answering with a decimal.

A) P(red hair):  

B) P(blue eyes):  

C) P(brown hair brown eyes):  

D) P(black hair blue eyes):  

E) P((brown hair)^c):  

F) P(brown eyes | red hair):  

G) P((red hair)^c | blue eyes):

Solution

a) P(red Hair) = 58/1971 = 0.02942
b) P(Blue Eyes) = 1223/1971 = 0.6205
c) P(brown hair brown eyes) = 893/1971 = 0.45306
d) P(black hair blue eyes) = P(black hair) + P( blue eyes) - P(black hair n blue eyes) = (811+1223 - 300)/1971 = 0.8798