For high school students, college admissions to the nation’s most selective univ
ID: 3371471 • Letter: F
Question
For high school students, college admissions to the nation’s most selective universities is very competitive. For example, it was reported in 2015 that elite school A accepted about 12% (.12) of its applicants, and elite school B accepted 11% (.11). Joanna has applied to both schools. Assuming that she is a typical applicant, she figures that her chances of getting into both A and B must be about 1.32% (.0132). a. How did she arrive at this conclusion? b. What additional assumption is she making? c. Do you agree with her conclusion? d. Suppose the conditional probability of getting into B, given you are already accepted into A, is .6. Now what is the probability of getting into both A and B?
Explanation / Answer
P(A)=0.12
P(B)=0.11
a) she multiplied both the probabilities. i.e
P(A)*P(B)=.12*.11 =0.0132
b) SHE is assuming that both A and B are independent events.result of one event is not affected by other because for independent events
P(A.B)= P(A)*P(B)
C) though it seems correct as admission in one college does not determined by other college.but sometimes depends on other criterion
d) FOR CONDITIONAL PROBABILITY
P(B/A)=P(A.B)/P(A)
PROBABILITY OF GETTING IN BOTH=P(A.B)= P(B/A)*P(A)
=.6*.12
=.072
=7.2%
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