Question 1119061
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Assume you have applied to two different universities (let's refer to them as Universities A and B) for your graduate work. 
In the past, 25% of students who applied to University A were accepted, while University B accepted 35% of the applicants. 
Assume events are independent of each other. 
Give all the answers as DECIMAL NUMBERS! 


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a.  What is the probability that you will be accepted in both universities? 


    P(A & B) = P(A)*P(B) = 0.25*0.35 = 0.0875.



b.  What is the probability that you will be accepted to at least one graduate program? 


    P(A U B) = P(A) + P(B) - P(A)*P(B) = 0.25 + 0.35 - 0.0875 = 0.5125



c.  What is the probability that one and only one of the universities will accept you? 


    P(A\B) + P(B\A) = P(A U B) - P(A & B) = 0.5125 - 0.0875 = 0.425.



d.  What is the probability that neither university will accept you? 


    1 - P(A U B) = 1 - 0.5125 = 0.4875.
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Solved.


All questions are answered.