Mythical Lady

“I don't know how to tell you this, but in my opinion, all but the last two sentences are wrong.

I want to check the correct use of the underlned verbals in the following sentences:

(probable+infinitive) From "It's probable that the disease is epidemic", can I say "The disease is probable to be epidemic"?  No.

The cat is probable to be out of the bag (does it convey the idiomatic meaning?)

It's probable to be rainy today.

Sorry, I've never heard this usage.  I'm used to "X is probable," and "It is probable that X will etc."

I'm quite used to ("Likely" + infinitive).  You may substitute "likely"  for  "probable" in all of your above examples.

(bound + that) It's bound that Mary applies for the job.  "It's imperative that Mary apply for the job."  "It's predetermined that Mary apply for the job."

Bad luck again.  To me, ("bound" + "that")  shows the determination of a person.  "Mary is bound that her son is going to graduate highschool."

"It's bound" takes the infinitive, in my experience.  "If you keep raising the pressure on that tire, it's bound to explode."

(there+seem) There seems to be a hoopoe in the garden.  Correct!

(certain+infinitive) It's certain to snow today

                           The *** is certain to hit the fan.  Correct!”

"Probable" is used in medical diagnosis in a strange way, but not with the infinitive.

"In my opinion, she is probable for Hepatitis A."  It sounds like an adjective, but I wouldn't swear to it.  It may be a new usage in certain technical disciplines.  Perhaps your very first one is correct, as a medical "diagnosis."  (Could we say, "epidemiological"?)

BTW, how does "probable" get to be a verbal??  It seems like all your underlined words (except the finite verb seems) are adjectives, and not ones which are derived from verbs.