I.
What is the probability of winning the lottery?
How good a chance do you have of winning the lottery?
How much chance do you have of winning the lottery?
What chance do you have of winning the lottery?
II.
Q: “How much of that milk are you going to drink?”
A: “Another glass.”
Q: “How much of the money is left?”
A: “None.”
Q: “How good is that ice-cream?”
A: “very good.”
Q: “How bad is his illness?”
A: “It is too bad.”
Please correct them.
If you wrote all these, then very good. Everything is correct, except that “It is too bad” is not a very natural response here. “It’s very bad” is more likely. (There is also a typo where you forgot to capitalise “very”.)
Dozy,
Can I rewrite this sentence : “How good a chance do you have of winning the lottery?”
as “How good a chance do you have for winning the lottery?”
or as “How good a chance do you have from winning the lottery?”?
“of” is the usual and natural choice. The others do not really sound correct, and there is no reason to want to use them.