Question 1119061: 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!
a. What is the probability that you will be accepted in both universities?
b. What is the probability that you will be accepted to at least one graduate program?
c. What is the probability that one and only one of the universities will accept you?
d. What is the probability that neither university will accept you?
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
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!
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.
Solved.
All questions are answered.
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