28. From the below cross classification showing the frequencies of hair and eye
ID: 2949774 • Letter: 2
Question
28. From the below cross classification showing the frequencies of hair and eye color of a group of staff at ABC company, and answer the following questions (a-d).
Eye Color
Hair Color
Brown
Blue
Green
Hazel
Total
Blond
30
20
7
3
60
Brown
74
28
10
7
119
Red/Auburn
17
15
5
4
41
Black
43
11
5
1
60
Total
164
72
27
14
280
a)The probability that a staff will have blue eyes given he/she is blond.
b)The probability of black hair
c)The probability that a staff will have either red hair or green eyes.
d)The probability that a staff will have brown hair and brown eyes.
Eye Color
Hair Color
Brown
Blue
Green
Hazel
Total
Blond
30
20
7
3
60
Brown
74
28
10
7
119
Red/Auburn
17
15
5
4
41
Black
43
11
5
1
60
Total
164
72
27
14
280
Explanation / Answer
a) P(Blue | Blond) = 20/60 = 0.3333
The probability that a staff will have blue eyes given he/she is blond is 0.3333
b) P(Black) = 60/280 = 0.2143
The probability of black hair is 0.2143
c)
P(Red hair OR Green eyes)
= P(Red hair) + P(Green eyes) - P(Red hair AND Green eyes)
= 41/280 + 27/280 - 5/280
= 63/280
= 0.2250
The probability that a staff will have either red hair or green eyes is 0.2250
d) P(Brown hair AND Brown eyes)= 74/280 = 0.2643
The probability that a staff will have brown hair and brown eyes is 0.2643
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