Hon tror på lyckan.

Hon is the subject form of she.

• Hon tror på lyckan. = She believes in luck / fortune.
• Jag ser henne. = I see her.

So here, because she is the one doing the action, Swedish uses hon.

Tror is the present tense of the verb tro, meaning to believe or to think.

A few useful forms are:

• infinitive: tro
• present: tror
• past: trodde
• supine: trott

One important thing for English speakers: Swedish verbs do not change for person.

• jag tror = I believe
• du tror = you believe
• hon tror = she believes
• vi tror = we believe

The verb stays tror in all those cases.

Because tro på is a very common Swedish combination meaning to believe in.

Compare:

• tro på något/någon = believe in something/someone
• tro att ... = think/believe that ...

Examples:

• Jag tror på dig. = I believe in you.
• Jag tror att hon kommer. = I think she is coming.

So in Hon tror på lyckan, the på is not optional. It belongs with tro here.

Lyckan is the definite singular form of lycka.

• lycka = luck / happiness / fortune
• lyckan = the luck / the happiness / the fortune

Swedish usually puts the definite article at the end of the noun instead of using a separate word like the.

So:

• en lycka = a luck/fortune/happiness
• lyckan = the luck/fortune/happiness

The -n is the definite ending.

It is built into lyckan.

In English, you say the luck or the fortune with a separate word.
In Swedish, the noun usually takes a suffix instead:

• bok = book
• boken = the book

The same pattern happens here:

• lycka
• lyckan

So there is no separate Swedish word before lyckan for the.

This is mostly about Swedish usage and style. With abstract ideas, Swedish often uses the definite form in places where English may use a more general form.

So tro på lyckan can mean believing in luck/fortune as a force or concept.

Using lycka without the definite ending would sound less natural in this kind of sentence. The definite form helps make it sound like a known idea: luck, fortune, fate-like good fortune.

That is a very good question.

In everyday Swedish:

• tur is the most common word for luck in the sense of chance
• lycka often means happiness, or sometimes good fortune

So Hon tror på lyckan can sound a bit more abstract, literary, or philosophical than Hon tror på tur.

Very roughly:

• tur = luck, chance, good luck
• lycka = happiness, fortune, blessedness, sometimes luck in a broader sense

So if you saw this sentence translated as She believes in luck, that is possible, but the Swedish word has a slightly broader tone than everyday tur.

This sentence has normal Swedish main-clause word order:

Hon + tror + på lyckan

That is:

• subject
• finite verb
• rest of the sentence

But Swedish main clauses follow the V2 rule, which means the finite verb normally comes in the second position.

For example:

• Hon tror på lyckan.
• Ibland tror hon på lyckan.

In the second sentence, Ibland comes first, so tror still stays in second position, and hon moves after it.

You usually put inte after the finite verb in a main clause.

So:

• Hon tror på lyckan. = She believes in luck.
• Hon tror inte på lyckan. = She does not believe in luck.

That placement of inte is very important in Swedish.

In a yes/no question, Swedish often puts the finite verb first:

• Tror hon på lyckan? = Does she believe in luck?

So you can compare:

• statement: Hon tror på lyckan.
• question: Tror hon på lyckan?

That verb-first pattern is very common in Swedish questions.