I believe your odds would be about the same as most permit applications ask if you would be willing to take a cow tag instead of a bull. Also even if you happen to get a cow tag ( here at least ). You can swap to another zone if anyone is looking for a swap which could have you end up with a bull tag in the end..

I have a friend who had a moose permit but could not hunt that year because his wife was sick with cancer. So he had asked about it and they had gave him the following year to hunt for one.. That was quite reasonable of them in my opinion anyway..