Y by Adventure10
Juli is a mathematician and devised an algorithm to find a husband. The strategy is:
• Start interviewing a maximum of
prospective husbands. Assign a ranking
to each person that is a positive integer. No two prospects will have same the rank
.
• Reject the first
men and let
be highest rank of these
men.
• After rejecting the first
men, select the next prospect with a rank greater than
and then stop the search immediately. If no candidate is selected after
interviews, the
person is selected.
Juli wants to find the value of
for which she has the highest probability of choosing the highest ranking prospect among all
candidates without having to interview all
prospects.
(a) (6 points:) What is the probability that the highest ranking prospect among all
prospects is the
prospect?
(b) (6 points:) Assume the highest ranking prospect is the
person to be interviewed. What is the probability that the highest rank candidate among the first
candidates is one of the first
candidates who were rejected?
(c) (6 points:) What is the probability that the prospect with the highest rank is the
person and that Juli will choose the
man using this algorithm?
(d) (16 points:) The total probability that Juli will choose the highest ranking prospect among the
prospects is the sum of the probability for each possible value of
with
ranging between
and
.
Find the sum. To simplify your answer use the formula

(e) (6 points:) Find that value of
that maximizes the probability of choosing the highest ranking prospect without interviewing all
candidates. You may need to know that the maximum of the function
is approximately
, where
is a constant and
is Euler’s number, 
• Start interviewing a maximum of



• Reject the first



• After rejecting the first




Juli wants to find the value of



(a) (6 points:) What is the probability that the highest ranking prospect among all


(b) (6 points:) Assume the highest ranking prospect is the



(c) (6 points:) What is the probability that the prospect with the highest rank is the


(d) (16 points:) The total probability that Juli will choose the highest ranking prospect among the





Find the sum. To simplify your answer use the formula

(e) (6 points:) Find that value of







This post has been edited 1 time. Last edited by soyeb.jim, Mar 3, 2018, 2:04 PM