If $X\sim F(m,n)$ then $1/X\sim F(n,m)$

If X is $F(m,n)$ (F-distribution with $m$ and $n$ degrees of freedom) and Y is $F(n,m)$, given that $P[X\ge c]=a$ then $P\bigl[Y\ge\tfrac1c\bigr]$ is: