S01E06: Dropping Gold Biscuits

Question:

If you have 1000 houses in a line, and you drop 1000 bombs randomly one by one, how many houses are likely to survive? or let’s say you have 1000 houses and you drop 1000 gold biscuits randomly, how many houses will not receive any gold biscuit at all?

Additional Questions:

If some houses are receiving more gold biscuits then other houses, what is the highest number of gold biscuits that one or more houses will receive?

If we conduct one more round of dropping these gold biscuits what will be the change observed in number of empty houses vs number of houses which received atleast one gold biscuit?

How many gold biscuits should be dropped to ensure all the houses receive atleast one gold biscuit? or How many rounds (of 1000) of dropping should be conducted to ensure this?

Instead of dropping completely randomly, can we change this to make the distribution more efficient also without keeping complete track of which houses have or have not received any gold biscuits?

How should I change my number of biscuits or number of houses to ensure that when I drop biscuits randomly, no house should have more than one gold biscuit?

Coding Assignments:

Create simulations of these questions and observe the outputs carefully.

Plot different graphs and analyze the relationship between number of houses and biscuits dropped.

Create a program for a more effiecient way of distribution and analyze how that performs (simple yet effective).

Derive formulas for all these questions emperically and verify them mathematically if possible.

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