Probability Involving AND and OR

[Derivator]

Hi folks,

Homework Statement

At Roanoke College it is known that 1/3
of the students live off campus. It is also known that 5/9
of the students are from within the state of Virginia and that 3/4
of the students are from out of state or live on campus. What is the
probability that a student selected at random from Roanoke College is from out
of state and lives on campus?

Homework Equations

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The Attempt at a Solution

It should yield:
P(out off state OR lives on campus) = P(out off state) + P(lives on campus) - P(out off state AND lives on campus)
thus
P(out off state AND lives on campus)
= P(out off state)+P(lives on campus)-P(out off state OR lives on campus)
=(1-5/9)+(1-1/3)-(3/4)
=4/9 + 2/3 - 3/4
=13/36
Is this correct?

-derivator

 

[RoshanBBQ]

Yes.

 

[Derivator]

thanks

 

[HallsofIvy]

The phrase should be "out of state", not "out off state".