as far as computer science is concerned, is discrete mathematics or probability and statistics more important?

Discrete math. No doubt. It has TONS of connections with computer science. Computer science (not computer programming mind you) is the theoretical study of discrete computation. They are highly connected -- for many subjects, the overlap between the two fields encompasses the entire subject, and it's impossible to tell where combinatorics ends and computer science begins.

To give some historical context though, discrete mathematics (also called combinatorics) were not necessarily their own subject for many years. The theories of probabilities were studied extensively as real-world problems (you know, gambling). In order to compute probabilities, combinatorics came about, since:

P[ winning ] = [ # possible win scenarios ] / [ # scenarios ]

in any gambling type game (assuming each scenario is equally likely). However, combinatorics eventually became a subject of study in its own right (and eventually, probability was demoted to "tool" status, instead of the other way around).

Statistics are essentially probabilities applied to data. Most of what you study in introductory statistics are the probabilities that certain types of data are "random" or "not random" (if it is "not random" then a correlation exists, or some other conclusion can be drawn). Statistics are used extensively in physical sciences and social sciences for data analysis.

But computer science doesn't have much of a connection to statistics, at least not compared to its connection with combinatorics. The two are virtually the same field, in many ways. Studies of computational complexity, algorithms, graph theory, linear and non-linear programming, finite state automata, I could go on and on about different sub-topics that both combinatorics and computer science include.

risk is the learn of "threat". "How probably is it that I do X and Y happens?" as an occasion: If I draw a card from a time-honored deck, what's the risk that it has a face on it? statistics is in many circumstances approximately attempting to degree something in a inhabitants according to a pattern. case in point, using statistics you'll be able to desire to ask what result's a smart cost of failure in a type of sunshine bulbs if the corporation claims a 5,000 hour advise time-to-failure, and what stated cost of failure is so unreasonable which you make certain the corporation's declare is faulty. Discrete arithmetic can incorporate some risk and statistics, besides the incontrovertible fact that that's greater in many circumstances relating to the maths that gets refrained from non-end concepts (for this reason "discrete"). some matrix arithmetic and purposes, and a few purposes of applications without calculus are what I remember.

I'd imagine discrete. As a computer is inherently a discrete system.

Probability/Stats might be useful in some specific situations, I think discrete would be more helpful in a wider range of applications