Learn Hardcore Spanish (Spain): Estoy seguro de que mi hermana aprobará; ya no estoy tan preocupado. - I am sure that my sister will pass; I am not so worried anymore.

In Spanish, estar is used for states or conditions (often temporary or linked to a specific situation), while ser is used for more permanent characteristics.

Estoy seguro = I am sure (about this particular thing / in this situation).
Soy seguro is almost never used in this sense. If used, it would sound odd and could be interpreted as something like I am a safe (reliable) person, but even that is unusual; normally one would say soy una persona segura (de mí misma).

So when expressing certainty about something, always use:
Estar seguro de que… = to be sure that…

Why is it “seguro” and not “segura”? What changes if the speaker is a woman?

Seguro / segura agrees with the speaker, not with mi hermana.

If the speaker is a man:
Estoy seguro de que mi hermana aprobará.
If the speaker is a woman:
Estoy segura de que mi hermana aprobará.

The rest of the sentence stays the same. The same thing happens later with preocupado / preocupada:

Male speaker: ya no estoy tan preocupado.
Female speaker: ya no estoy tan preocupada.

Why do we say “estoy seguro de que” and not just “estoy seguro que” or “estoy seguro de”?

The standard, most correct form is:

Estar seguro de que + [clause]

So:

Estoy seguro de que mi hermana aprobará.

Notes:

“Estoy seguro de que” is what you should use in formal and careful Spanish.
“Estoy seguro que…” is common in spoken Spanish, but many speakers consider it less correct or more colloquial.
“Estoy seguro de” is used if you follow it with a noun / pronoun, not a full clause:
- Estoy seguro de su aprobado. = I’m sure about her passing (the exam).
- Estoy seguro de ello. = I’m sure of it.

So with a full sentence after it, use de que.

Could you say “estoy seguro mi hermana aprobará” without “de que”?

No. In standard Spanish, that would be incorrect or at least sound very wrong.

After estar seguro, when you introduce a full clause (subject + verb), you need a connector:

Estoy seguro de que mi hermana aprobará.

Leaving out de que is not natural Spanish in this structure.

Why is it “aprobará” (future tense) and not something like “aprueba” or “va a aprobar”?

All three exist in Spanish, but they have different nuances:

Aprobará – simple future tense.
Here it expresses a future event that the speaker is sure about:
I’m sure my sister will pass.
Va a aprobar – periphrastic future (going to future).
Very common in spoken Spanish and also correct:
Estoy seguro de que mi hermana va a aprobar.
This can sound a bit more like it’s (practically) arranged / it’s going to happen.
Aprueba – present tense.
Estoy seguro de que mi hermana aprueba normally sounds odd in this context.
Present is not usually used for a future exam result, unless you have a very specific time context or structure (e.g. timetable: El examen lo aprueba o no lo aprueba hoy).

In your sentence, aprobará is the most natural choice to talk about a result in the future that you are sure about.

Why isn’t it “apruebe” (subjunctive) after “estoy seguro de que”?

Whether you use the indicative or subjunctive after a phrase of opinion/belief depends on the degree of certainty:

Estoy seguro de que… = I am sure that…
→ you express certainty → use indicative:
Estoy seguro de que mi hermana aprobará.
No estoy seguro de que… = I am not sure that…
→ you express doubt → use subjunctive:
No estoy seguro de que mi hermana apruebe.

So:

Estoy seguro de que aprobará (indicative) = I’m sure she will pass.
No estoy seguro de que apruebe (subjunctive) = I’m not sure she will pass.

That’s why “apruebe” would be wrong in your original sentence.

What exactly does “aprobar” mean here? Does it mean “to approve” like in English?

In Spain, aprobar is the usual verb for passing an exam, class, or test:

Mi hermana aprobará ≈ My sister will pass (the exam / the course).

In many Latin American countries, aprobar more commonly means to approve (in the sense of authorise, accept, vote in favour), and pasar or other verbs are used for exams. But in Spain:

aprobar un examen / una asignatura / el curso = to pass an exam / a subject / the school year.

What does “ya no” mean in “ya no estoy tan preocupado”?

Ya no means “no longer / not anymore”.

Ya no estoy tan preocupado.
= I’m not so worried anymore / I’m no longer so worried.

Related forms:

todavía no = not yet
- Todavía no estoy tranquilo. = I’m not calm yet.
ya (without no) often means already / now:
- Ya estoy tranquilo. = I’m already calm / I’m calm now.

So ya no always adds the idea that a previous state has stopped.

Why is the word order “ya no estoy tan preocupado” and not “no ya estoy tan preocupado”?

In Spanish, no must go directly before the conjugated verb:

no estoy (not estoy no or no ya estoy).

Adverbs like ya go before no + verb or after the verb, depending on meaning and emphasis. The natural pattern here is:

ya no + [verb] = no longer
- verb
  → ya no estoy tan preocupado.

You could say no estoy tan preocupado ya, but that has a slightly different rhythm and often less emphasis on the change; ya no estoy… is the most standard for I am no longer….

What is the difference between “tan preocupado” and “muy preocupado”?

Both can intensify the adjective, but they’re used a bit differently:

tan preocupado
- Literally “so worried”, often linked to comparison or reference.
- Common in:
  - Comparisons: tan preocupado como antes = as worried as before.
  - Changes: ya no estoy tan preocupado = I’m not as worried as before / not so worried anymore.
muy preocupado
- “very worried”, pure intensity:
  - Estoy muy preocupado. = I’m very worried.

In your sentence, tan hints at a comparison with an earlier state: I used to be more worried; now I’m not so worried (not as much as before).

Why does “preocupado” end in -o and how would it change for a woman or for plural?

Preocupado is an adjective and must agree in gender and number with the subject (yo):

Male speaker, singular:
- (Yo) estoy preocupado.
Female speaker, singular:
- (Yo) estoy preocupada.
Group of only men or mixed group:
- (Nosotros) estamos preocupados.
Group of only women:
- (Nosotras) estamos preocupadas.

So, for a woman saying the original sentence:

Estoy segura de que mi hermana aprobará; ya no estoy tan preocupada.

Could the subject pronoun “yo” be included in “estoy seguro”? Does it change the meaning?

Yes, you can say:

Yo estoy seguro de que mi hermana aprobará; ya no estoy tan preocupado.

Including yo doesn’t change the basic meaning. Spanish usually omits subject pronouns because the verb ending already shows the person (here, -oy in estoy = first person singular).

You add yo mainly for:

Emphasis:
Yo estoy seguro… = I am sure (maybe others are not).
Contrast with someone else:
Yo estoy seguro, pero mi madre no. = I am sure, but my mother isn’t.

In neutral, non-contrastive sentences, leaving it out is more natural: Estoy seguro…

Is the semicolon ( ; ) used in Spanish the same way as in English here?

Yes, very similar.

The semicolon in:

Estoy seguro de que mi hermana aprobará; ya no estoy tan preocupado.

connects two closely related ideas that could be separate sentences:

Estoy seguro de que mi hermana aprobará.
Ya no estoy tan preocupado.

In Spanish you could also write:

With a full stop:
Estoy seguro de que mi hermana aprobará. Ya no estoy tan preocupado.
With a comma + y:
Estoy seguro de que mi hermana aprobará, y ya no estoy tan preocupado.

All are correct; the semicolon just marks a slightly stronger separation than a comma, but closer connection than a full stop.