Hair Color of Randomly Selected Individuals Trait Brown (BR) Black (BL) Other (O
ID: 3431212 • Letter: H
Question
Hair Color of Randomly Selected Individuals
Trait
Brown (BR)
Black (BL)
Other (O)
Total
Yes (Y)
20
47
13
80
No (N)
75
13
32
120
Total
95
60
45
200
Certain trait associated with hair color.
What is the probability that individual selected has:
A)The trait or black hair
B)Does not have the trait given that they have black hair
C)Brown hair and does not have the trait
Are events Y and BL:
A)Mutually exclusive? (explain)
B)Independent? (provide proof)
Answer in great detail with formulas that were used to solve each part of question. Written by hand given preference.
Trait
Brown (BR)
Black (BL)
Other (O)
Total
Yes (Y)
20
47
13
80
No (N)
75
13
32
120
Total
95
60
45
200
Explanation / Answer
What is the probability that individual selected has:
A)The trait or black hair
P(trait or black hair) = P(trait) + P(black hair) - P(both)
=80/200 + 60/200- 47/200
=0.465
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B)Does not have the trait given that they have black hair
P(not trait | black hair) = P(not trait and black hair) / P(black hair)
=13/60
=0.2166667
--------------------------------------------------------------------------------------------------------------------------
C)Brown hair and does not have the trait
P(brown hair and not trait) =75/200 =0.375
--------------------------------------------------------------------------------------------------------------------------
Are events Y and BL:
A)Mutually exclusive? (explain)
No, because P(Y and BL) is not equal to 0
--------------------------------------------------------------------------------------------------------------------------
B)Independent? (provide proof)
No, because P(Y and BL) =47/200 is not equal to P(Y)*P(BL) =(80/200)*(60/200)
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