One of the most effective recruiting techniques to the Virginia Tech Honors prog

Question

One of the most effective recruiting techniques to the Virginia Tech Honors program is getting the students to visit the campus before making their decision. According to recent data, 45% of the potential honors students visit the campus before making their decision. If the student visits, they accept the offer to attend Virginia Tech 95% of the time, but the students that do not visit the campus before making their decision will attend 55% of the time. Knowing a student will enter the Virginia Tech Honors program, what is the probability that they visited the campus before making their decision? (note: all data is fictional)

Explanation / Answer

Given P(visit)=0.45, P(not visit)= 1-P(visit)=1-0.45=0.55           P(attend |visit) =0.95           P(attend |not visit) = 0.55 The probability is P(visit | attend) =P(visit and attend)/P(attend) =0.45*0.95/(0.45*0.95+0.55*0.55) = 0.5856164

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