False positive number Bloom filter
Yes, and it is very simple.
Count the number of bits that are 'on' and divide that by the total number of bits. This will give you your fill-rate. 
When querying, all elements that were inserted earlier will hit 'on' bits and return positive. For elements which were not inserted into the filter, the probability of hitting an 'on' bit is your fill-rate. Therefore, with 3 hash functions, your error-rate will be (fill_rate^3).
Though 0.5 is the optimal fill-rate that maximizes space vs. error-rate, any other fill rate is possible but it will either take too much space or has a higher error-rate than required. So you may be better off using 4 hash functions with less space. It really depends on your use case. What is your requirement? what error-rate are you looking for?
I implemented a bloom filter with 3 hash functions, and now I should calculate the exact number of false positives (not possibility) in that filter. Is there an efficient way to calculate that? The number of items in the filter is 200 million and the size of bit array is 400 million