Any particular reason the numbers used are so awkward?
Best to answer the final question, and then you are free to insert whatever the heck numbers you like. The answer is going to be based on the "binomial distribution", which gives that if an event either happens (with probability z) or does not (with probability 1-z), then the probability of k occurences of the event in N trials is:
{N!/[k! (N-k)!]} *z^k*(1-z)^(N-k)
where N! means "N factorial" and, say, 4! = 4*3*2*1 = 24; and p^k is p to the power of k. To adapt to the case you are interested in when you want, say, q% successes or greater out of the N times you throw it, then you would replace k in the formula above by k=(q*N/100), and then sum between this value of k and k = N.
It ain't pretty, I'm afraid. To get a handle on what you might expect, though, if we take N = 100 trials, z = 43% and q = 44%, then the probability that you got more than 44/100 tails is about 45%.