18 made the eans it Of he entering class at a college, 73% attended public high

Question

18 made the eans it Of he entering class at a college, 73% attended public high school 1 % attended private hi h s hoo and 8 were home sc o e Of o e no attend public i 15% of those who attended private high school made the Dean's list, and 19% of those who were home schooled made the Dean's list. A student is randomly chosen. a) Find the probability that the student made the Dean's list. b) Find the probability that the student came from a public high school, given that the student made the Dean's list. c) Find the probability that the student did not attend private high school, given that the student did not make the Dean's ist. scho a) The probability that the student made the Dean's list is (Do not round until the final answer. Then round to four decimal places as needed.) b) The probability that the student came from a public high school, given that the student made the Dean's list, is Do not round undilthe final answer: Then round to four decimal laces as neded.) c) The probability that the student did not attend private high school, given that the student did not make the Dean's list, is (Do not round until the final answer. Then round to four decimal places as needed.)

Explanation / Answer

from abvoe:

a)P(made the Dean's list)=P(public high school and Dean's list+Private high school and Dean's list+Home school and Dean's list)=0.73*0.16+0.19*0.15+0.08*0.19=0.1605

b) P(public high school|Dean's list) =P(public high school and Dean's list)/P(Dean's list)

=0.73*0.16/0.1605=0.7277

c)

P(not private high scool |not in Dean's list) =(0.73*(1-0.16)+0.08*(1-0.19))/(1-0.1605)=0.8076

( please revert for any clarification)

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