* Please explain your answer ! A new web service decides to use a program called

Question

* Please explain your answer !

A new web service decides to use a program called BinCodes to generate coupon codes
for its customers. BinCodes generates 10 digit binary strings as coupon codes where each
digit is 0 or 1 uniformly at random. If two users get the same coupon code, one of them
cannot use it and must be refunded one dollar for the inconvenience. If BinCodes is used
to generate a coupon code for all of the 5000 customers, how many dollars in total are
expected to be refunded to users due to such collisions?

Explanation / Answer

Look total unique ticket possibilities - 210 = 1024 .

Now leaving 1024 tickets every ticket will be refunded .

So for 5000 customers, only 1024 people won't have to get refund. Rest all will get refunds,

ie. 5000 - 1024 = 3976$

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