Look at neuroscience oriented studies. e.g. Antonio Damasio: Descartes Error, Oshin Vartanian and David Mandel (eds): Neuroscience of Decision Making, and Esther Thelen and Linda Smith: A Dynamic Systems Approach to the Development of Cognition and Action.  Avoid snake oil salespersons esp economists

Sajad, you are talking about attitude to lottery. Typically von Neumann expected utility is used for risk attitude; see https://en.wikipedia.org/wiki/Expected_utility_hypothesis . While it may capture different levels of risk aversion, it is linear functional of probability vector. I think that empirical puzzle is that we do not necessarily behave like this. People tend to overestimate or underestimate some risks. Our perception of premium for unlikely events (that happen 1/1000 or less) is not captured by probability. We often prefer an event without them completely rather such lottery with a barrel of honey and a spoon of dirt.

In practice people have wrong perception of risks; see this graph from http://www.colorful-data.net/ Maybe this is the reason that we do not trust any probability but add some error of measurement around it. This spoils more perceived value of lotteries where bad outcome has low probability.

Expected utility is nonsense when it comes to life situations.  It assumes independence from states of nature but life fails the test. Either you ignore life or ignore certainty equivalence.  I think the great von Neumann was talked into this by stupid economists who use mathematics but refuse to learn it .  He would not have one that to physics, because nature is unbridgeable.  A good place to look for good statistical analysis is small particle physics. Besides: Expected value never happens any way. Ask the Santa Fe Institute guys about the "lantern Bar"

Brains do not have an arithmetic logical unit ALU like computers in their CPU. In brains association processes cause results and not logical decisions.

If we think about our own wins, we do not really think in terms of probability. We think much more about "having chance" as subject of our superstitions. The reason of the first choice is something like "as normally I don't have chance, I take for sure 3000 $". The reason of the second choice is "One chance of four or one chance of five is almost the same thing. So, if I should have the chance to win this time (and in this premize the probability does not play any role, anymore) then I prefer a bigger win."

The situation is even more complicated as the win expectation in the situation 20 % for 4000 $ is 800 $, while in the situation 25 % of 3000 $ is only 750 $. When asking about the logical reaction, one can suppose that there is always a consistent theory of best decision. I don't believe that such a theory can really exist. The situation is similar to Arrows result about the impossibility to centralize priority lists which are built on different criteria.

There are timid and bold characters. This basic setting takes more influence in the decision making process than logical thinking. 

There are more individual factors which cannot be quantified. Nevertheless a statistical result can be found but it is not able to interpret an individual case.

Perhaps, Sajad, our decision making isn't logical, because logic is propositional. Propositions are not natural. A proposition is a mental proposal suggesting an impossibility after which there remains one (non-mental) possibility.

For the most part, a proposition is a vicarious struggle symbolized by the non-survivable superposition of several things we must have, yet only one of which may survive. "Here are two of Everything; which one should survive?" There cannot be two of everything, but the mind demands we imagine that. So this kind of ultimatum is not a natural moment for us, requiring we suspend reality and manipulate an artificial world inside.

More poignantly, we cannot endure the proposition that something of qualitative value might perish (a kind of empathy beneath this demanding, quantifying cognition). This is very evident in the hoarding disorder, in which persons cannot choose between the fates of our discards (because they feel like one). Consider that we are not rational equation solvers, just living things. Consider that we are affective creatures, not cognitive or logical mechanisms. Calculations are meaningless in nature, and require a temporary suspension of awareness to carry them out.

What we call paradox, to me, is a sudden glimpse of things we really and truly need or value but which do not conform to our ambivalent reasoning systems (see Triver's parental investment theory, which tries to explain paradoxes that natural selection cannot, and which paradoxes Darwin's sexual selection theory used to try and explain. We often choose non-survivable options).

Paradox arises from propositions of any kind (also see Kurt Godel) -- even so simple a thing as to decide, when we suddenly discover we cannot choose while our decision stands.

Michalski, R. L., & Shackelford, T. K. (2010). Evolutionary personality psychology: Reconciling human nature and individual differences. Personality and Individual Differences, 48(5), 509-516. doi:http://dx.doi.org.lopes.idm.oclc.org/10.1016/j.paid.2009.10.027

Sorry, but I don't see the two cases as being exactly the same and, therefore, the decision is not necessarily without logic.

While Task 2 is clearly based upon statistics, Task 1 is not exactly so.

If we talk about statistics, Task 1 should say that, based upon, say, 2000 cases, 100% of the 1000 who chose 3000$ got it, while only 80% of the 1000 who chose 4000$ got it. This way, the better chance still leaves room for some risk.

Instead, when you say "for sure," I think we all understand that, if we choose 3000$, we just get without any risk, so (unless we are addicted gamblers), we decide to just get it.

I somehow agree with @Itzhak. While it's seem that first set is just second set with simple multiplication of chances, but even in formulation (like Fokker-Planck equation), there is a huge difference between "for sure" and "with some chance". It can be model with a simple random walk with given probability distribution but any deterministic formulation is not possible!