Unfair coin probability (P) that results in 0.5% chance of getting x tails out of y tosses?

Question

For an unfair coin toss that produces heads with probability P, what is the value of P that will result in 0.5% (i.e. 0.005) chance of getting exactly x tails out of y tosses?

i.e. is there a general solution to ${y\choose x}P^{y-x}(1-P)^x=0.005$ for $P?$

Answer 1

Since the probability of getting $x$ tails out of $y$ tosses is ${y\choose x}P^{y-x}(1-P)^x$, we just need to solve ${y\choose x}P^{y-x}(1-P)^x=0.005$ for $P.$