Question $4$ Submitted Mar $28$th $2024$ at $5$:$20$:$36$ pm

You are a software engineer at NiemaNet, a tech company that is in the process of releasing their own streaming service: Niemaflix. The NiemaNet executives were able to negotiate streaming rights for at most $10,000$ movies, and they ask you to build an app that enables users to search for whether or not a movie is available on Niemaflix. Being an Advanced Data Structures expert, you decide to use a Bloom Filter for this purpose. You search the internet and find $3$ hash functions that you want to use, and you decide to try using $10,000$ bytes to store your Bloom Filter flags.

Using the equation presented in this class, what is the probability of encountering a False Positive

when you search for a movie that isn't actually available on Niemaflix?

Note: The memory size we gave you is in bytes, not bits.

Note: If there is not enough information to answer the question, enter $-1$ as your answer.

Note: Enter your answer as a decimal rounded to $3$ decimal places. For example, if you believe the answer is $12\mathrm{.}35\%,$ enter your answer as $0\mathrm{.}124$