# W2 Sum of Expectations - Name Assignment EV

Hello,

The question’s summary is:
Given 8 billion people in the world, if we collect all of their names, what is the expected value of randomly assigning a name to its rightful owner?

I’m assuming that the names collected are unique, and that if a person picks out a name, they wouldn’t replace their selection (is this correct to assume?).

As a result, I defined the problem on a smaller space as follows.
100 people and 100 unique names without replacement:

• 1st person has 100 names to choose from - 1/100 chance they pick their name;
• 2nd person has 99 names to choose from - 1/99 chance they pick their name if not picked by previous 1 person; otherwise 0;
• 3rd person has 98 names to choose from - 1/98 chance they pick their name if not picked by previous 2 people; otherwise 0;
• 100th person has 1 name to choose from - 1/1 chance they pick their name if not picked by previous 99 people people; otherwise 0.

Does this approach make sense?