1. Assume you have applied to two different universities (University A and Unive
ID: 3242815 • Letter: 1
Question
1. Assume you have applied to two different universities (University A and University B) for graduate work. In the past, 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the applicants. Assume events are independent of each other.
a) Find the probability of getting acceptance letters for both universities P(A and B)
b) Find the probability of getting an acceptance letter for either university P(A or B )
c) State the probability of getting accepted to University A - - P(A)
d) State the probability of getting accepted to University B -- P(B)
e) Does it seem you should apply to only one of the universities, if so which one, or both universities? Explain.
Explanation / Answer
a) P(A and B) = P(A intersection B)
=> P(A) x P(B)
=> 0.25 x 0.35
=> 0.0875
B) P(A or B) = P(A U B)
=> P(A) + P(B) - P(A intersection B)
=> 0.25 + 0.35 - 0.0875
=> 0.5125
C) P(A) = 0.25
D) P(B) = 0.35
E) We should apply to both universities as the probability of getting admission in one of the universities [P(A or B)] is higher than getting selected in any one of the universities [P(A) or P(B)] . Hence, it is beneficial to apply in both the universities
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