Sample space of an experiment In any probabilistic model,do a finite sample space always corresponds to discrete sample space & an infinite sample space always corresponds to a continuous sample space and vice versa?

Finite implies discrete. 
But infinite does not imply continuous. For example, toss a fair coin until you get a head. Then the number of tosses can be $1,2,3,4,\dots$ but the distribution is discrete, not continuous. In general when the sample space is countable, then the distribution is discrete. 
Continuous does imply infinite.
Note that there are distributions that are neither discrete nor continuous.
