Lets say we have n coins and probability of Coin i to fall heads is f(i) . Find the probability of getting even number of heads when all the n coins are tossed.
f(i) = 1 / (2i + 3)
Here n is large, of the order of 1e5, so efficient approach is required.
I tried to analyse the brute force case but that would be too much i.e. If I calculate for 2 success, 4, 6..., it might take years to run.
Then I thought of applying Linearity of Expectation somehow but couldn't come up with anything which could help.