Researchers sampled 1971 German men to determine if there is a relationship betw

Question

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):

   Hair Color Eye Color Brown Black Red Total Brown 209 511 28 748 Blue 893 300 30 1223 Total 1102 811 58 1971

Explanation / Answer

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

BROWN BLACK RED BROWN 209 511 28 748 A1 BLUE 893 300 30 1223 A2 Totals 1102 811 58 1971 B1 B2

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