Question
In: Statistics and Probability
in a college in new jersey 1/3 of the students live off campus while 5/9 of...
in
a college in new jersey 1/3 of the students live off campus while
5/9 of the students live in new jersey. furthermore 3/4 of the
students live on campus or are not from new jersey. if a student is
selected at random from the college, what is the probAbility
a) student lives on campus and is not from new jersey
b) the student is not from new jersey provided they live on
campus
c) student lives on campus provided they arent from new
jersey
Solutions
Expert Solution
Given
P( a randomly selected student live off campus) = 1/3
That implies, P( a randomly selected student live on campus) = 1 - 1/3 = 2/3
P( a randomly selected student live new jersey) = 5/9
That implies, P(a randomly selected student does not live new jersey) = 1 - 5/9 = 4/9
P( a randomly selected student live on campus or are not from new jersey) = 3/4
a) The probability that a randomly selected student lives on campus and is not from new jersey
= P( a randomly selected student live on campus) + P(a randomly selected student does not live new jersey) - P( a randomly selected student live on campus or are not from new jersey)
b) The probability that a randomly selected student is not from new jersey provided they live on campus
= P(a randomly selected student does not live new jersey | a randomly selected student live on campus )
= P(a randomly selected student lives on campus and is not from new jersey) / P(a randomly selected student live on campus )
c) The probability that a randomly selected student lives on campus provided they arent from new jersey
= P(a randomly selected student live on campus | a randomly selected student does not live new jersey )
= P(a randomly selected student lives on campus and is not from new jersey) / P(a randomly selected student does not live new jersey )
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