4. A survey of a sample of business students resulted in the following informati
ID: 3046022 • Letter: 4
Question
4. A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major.
Gender
Management
Marketing
Others
Total
Male
25
20
30
75
Female
35
20
70
125
Total
60
40
100
200
Based on the data above, please compute the following probabilities.Show your work, NOT just answers.
(1)
What is the probability of selecting an individual who is majoring in Marketing?
(2)
What is the probability of selecting a male individual?
(3)
Given that a person is male, what is the probability that he is majoring in Management?
(4)
What is the probability of selecting an individual who is majoring in Marketing, given that the person is female?
Gender
Management
Marketing
Others
Total
Male
25
20
30
75
Female
35
20
70
125
Total
60
40
100
200
Explanation / Answer
(1) From the given Table,
P(Marketing) = 40/200 = 0.2
EXPLANATIONL Total for Marketing = 40. Overall total = 200
(2) P(Male) = 75/200 = 0.375
EXPLANATION: Total for Males = 75. Overall total = 200
(3) By Multiplication Rule:
P(Management/Male) = P(Management & Male)/ P(Male)
= 25/75 = 0.3333
(4) By Multiplication Rule:
P(Marketing/Female) = P(Marketing & Female)/ P(Female)
= 20/125 = 0.16
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