A pessimist is someone who always considers negative outcomes of a situation, whereas an optimist always considers the positive outcomes. Is there a word for someone who, in any given situation, doesn't care about the outcome at all?
I can't think of a noun, but you can say "that person is apathetic".
Apathetic at Oxford Dictionaries
adjective showing or feeling no interest, enthusiasm, or concern
late 14c., "unbiased," from Old French indifferent "impartial" or directly from Latin indifferentem (nominative indifferens) "not differing, not particular, of not consequence, neither good nor evil," [...] Extended sense of "apathetic" first recorded early 15c.; that of "neither good nor bad" 1530s, on notion of "neither more nor less advantageous."
This might not be quite what you are looking for, but as an extreme case:
This stems from following nihilism (adapted from the OED):
Total rejection of prevailing religious beliefs, moral principles, laws, etc., often from a sense of despair and the belief that life is devoid of meaning.
The belief or theory that the world has no real existence; the rejection of all notions of reality.
A nihilist would not care about an outcome because it is entirely meaningless.
The word has some negative connotations from meaning 1 above, which may make it unsuitable for your particular purpose.
free from concern, worry or anxiety
Unconcerned, undisturbed; carefree and nonchalant
Origin: 1820–30; < French, equivalent to in- in-3 + souciant present participle of soucier to worry < Vulgar Latin *sollicītāre, for Latin sollicitāre to disturb; see solicitous
as suggested in the definitions the other words I would prefer to use are:
All of these words imply a carefree attitude in a good way and lack the negative connotations of having no feeling at all.
A fatalist. This does not just mean a person who thinks all things are fated; it has a derived meaning: a person with an attitude of indifference to outcome because of such a belief. An optimist hopes for the best; a pessimist fears the worst; a fatalist is resigned to what will be (regardless of hopes and fears). http://www.merriam-webster.com/dictionary/fatalism
In modern Internet parlance, such a person might be referred to as a "honey badger":
This use of the term is based on this popular youtube video.
(Hat tip to user @balpha for bringing this oversight to my attention.)
That would be an apathist I think.
Carefree- having no worries
On the day of the result, Ajay, being optimistic, was very sure of securing all the A grades. But Arun's pessimistic mind was busy looking for excuses to tell his parents why he flunked this time. And Aakash remained as carefree as ever and kept playing video games throughout the day.
How about "this person is a stoic" ?
According to Merriam Webster:
Definition of STOIC ... 2 : one apparently or professedly indifferent to pleasure or pain
How about the adjective related to the word:
Does such an adjective exist in English by the way ??
Technically one could say a realist. However this probably isn't applicable to your situation.
A person who cares not at all about anything "in any given situation", must surely be...a cadaver.
More seriously, there are also mugwumps, sloths, and bumps-on-a-log, all of which have some of the qualities you describe.
(1)Selfish A man who doesn't care about anything must clearly be the most self absorbed person on the earth. And if he is not self absorbed then refer to answer #2 (2)Dead
Insouciant is a word in both the French and English language for a person who does not care about anything. In French it can be both an adjective & a noun. I don't see why one could not use it as a noun in English too. Such a person would be an insouciant. Such an noun is needed.
If you're looking for one who not only doesn't care about anything, but is in a general surly mood about things...there's "Misanthrope", and the adjective form, "Misanthropic".