A couple hires a typist to prepare invitations for their upcoming wedding. However, due to budget constraints, they end up underpaying the typist. Each invitation consists of an elegant card indicating the guest’s name, and an envelope that also has the guest’s name written on it. On the day that the typist was to receive her pay, both cards and envelopes have already been (separately) prepared, and the only remaining work was for her to put the cards in their respective envelopes. Disappointed with being shortchanged, she decides to put the cards into random envelopes. Assuming the typist did not intentionally put the cards into the wrong envelopes, and for each card was blindly choosing any random envelope (say, with eyes closed), on average how many cards are put into the right envelope? (Hint: assume ? is the number of guests. Take a variable ? where ? = 1 for a card that is put into the right envelope, and ? = 0 if not. The problem can be simplified by ignoring the order.)

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...
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A couple hires a typist to prepare invitations for their upcoming wedding. However, due to budget constraints, they end up underpaying the typist. Each invitation consists of an elegant card indicating the guest’s name, and an envelope that also has the guest’s name written on it. On the day that the typist was to receive her pay, both cards and envelopes have already been (separately) prepared, and the only remaining work was for her to put the cards in their respective envelopes. Disappointed with being shortchanged, she decides to put the cards into random envelopes. Assuming the typist did not intentionally put the cards into the wrong envelopes, and for each card was blindly choosing any random envelope (say, with eyes closed), on average how many cards are put into the right envelope? (Hint: assume ? is the number of guests. Take a variable ? where ? = 1 for a card that is put into the right envelope, and ? = 0 if not. The problem can be simplified by ignoring the order.)
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