1. A company hired 30 new college graduates last week. Of these, 16 are female a
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Question
1. A company hired 30 new college graduates last week. Of these, 16 are female and 11 are business majors. Of the 16 females, 9 are business majors. Can you draw the table? Hint: Male Female Total Other majorTotal 12 Business major 14 16 30 9 19 a. Are the events "female" and "business major" independent? b. Are the events "female" and "business major" mutually exclusive? Explain why or why not. c. find the probability that a randomly selected employee will be both male and business major d. find the probability that a randomly selected employee will be a male given he is a business major. d. find the probability that a randomly selected employee will be a male or a business major. e. find the probability that a randomly selected employee will be a male or female f. find the probability that a randomly selected employee will be a male and femaleExplanation / Answer
a) Here we have:
P( female ) = 16/30 = 0.5333
P( business major ) = 11/30 = 0.3667
P( female and business major ) = 9/30 = 0.3
P( female ) P( business major ) = 0.5333*0.3667 = 0.1956
Therefore P( female ) P( business major ) is not equal to P( female and business major )
Therefore the 2 events are not independent.
b) Clearly as P( female and business major ) is not equal to 0, therefore the two events here are not mutually exclusive.
c) P( male and business major ) = 2/30 = 0.0667
d) Given that he is a business major, probability that the employee would be male is computed here as:
P( male | business major ) = n( male and business major ) / n ( business major ) = 2/11 = 0.1818
d) P( male or business major ) = ( 14 + 11 - 2 ) / 30 = 23/30 = 0.7667
e) P( male or female ) = 1
1 is the required probability here.
f) P( male and female ) = 0
because a person cannot be both male and female.
Therefore 0 is the required probability here.
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