For high school students graduating in 2010, college admissions to the nation’s
ID: 3374608 • Letter: F
Question
For high school students graduating in 2010, college admissions to the nation’s most selective schools were the most competitive in memory. Harvard accepted only about 9% of the applicants, Stanford 10% and Penn 16%. John has applied to all three schools. Assuming that he is a typical applicant, and that admissions to the three schools are independent events, compute the following probabilities. a) What is the probability that John will be accepted at both Harvard and Stanford, but not at Penn? b) What is the probability that John will not be accepted by any of the three schools? c) What is the probability that at least one school will accept him? For high school students graduating in 2010, college admissions to the nation’s most selective schools were the most competitive in memory. Harvard accepted only about 9% of the applicants, Stanford 10% and Penn 16%. John has applied to all three schools. Assuming that he is a typical applicant, and that admissions to the three schools are independent events, compute the following probabilities. a) What is the probability that John will be accepted at both Harvard and Stanford, but not at Penn? b) What is the probability that John will not be accepted by any of the three schools? c) What is the probability that at least one school will accept him? For high school students graduating in 2010, college admissions to the nation’s most selective schools were the most competitive in memory. Harvard accepted only about 9% of the applicants, Stanford 10% and Penn 16%. John has applied to all three schools. Assuming that he is a typical applicant, and that admissions to the three schools are independent events, compute the following probabilities. a) What is the probability that John will be accepted at both Harvard and Stanford, but not at Penn? b) What is the probability that John will not be accepted by any of the three schools? c) What is the probability that at least one school will accept him?Explanation / Answer
a) probability that John will be accepted at both Harvard and Stanford, but not at Penn
=P(Harvard)*P(Stanford)*(1-P(Penn)) =0.09*0.10*(1-0.16)=0.00756
b)
probability that John will not be accepted by any of the three schools
=(1-P(Horward))*(1-P(Stanford))*(1-P(Pen))=(1-0.09)*(1-0.10)*(1-0.16)=0.68796
c)
probability that at least one school will accept him =1-P(none accepts)=1-0.68796=0.31204
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