Вероятность дождя сегодня высокая, поэтому я возьму зонтик.

Because вероятность normally takes the thing that is probable in the genitive.

So:

• вероятность дождя = the probability of rain
• вероятность снега = the probability of snow
• вероятность успеха = the probability of success

This is similar to English probability of ....

Высокая agrees with вероятность, which is:

• feminine
• singular
• nominative

So the adjective must also be feminine singular nominative:

• высокая вероятность
• вероятность ... высокая

That is why you get высокая.

In Russian, the verb to be is usually omitted in the present tense.

So:

• Вероятность дождя сегодня высокая
  literally = The probability of rain today high
• natural English = The probability of rain today is high

This is completely normal Russian. In the past or future, a form of быть would appear if needed.

Yes, it is natural. But Russian word order is flexible, so several versions are possible.

For example:

• Вероятность дождя сегодня высокая
• Сегодня вероятность дождя высокая
• Сегодня высокая вероятность дождя

All are understandable. The differences are mostly about emphasis:

• starting with сегодня emphasizes today
• starting with высокая вероятность дождя sounds a bit more like presenting the fact first

The original sentence is fine and natural.

Because the sentence has two clauses:

• Вероятность дождя сегодня высокая
• поэтому я возьму зонтик

Поэтому connects the second clause as a result of the first one, so a comma is normally written before it.

It works like therefore / so / that’s why in English.

Поэтому means therefore, so, that’s why, or for that reason.

In this sentence:

• Вероятность дождя сегодня высокая, поэтому я возьму зонтик.
• The chance of rain is high today, so I’ll take an umbrella.

It introduces a consequence or result.

Возьму is the perfective future of взять. It means a single completed action in the future: I will take.

Russian often uses:

• imperfective for process, repetition, or ongoing action
• perfective for one completed action

Here, taking the umbrella is a one-time action, so возьму is the normal choice.

Compare:

• я возьму зонтик = I’ll take an umbrella
• я буду брать зонтик = sounds like repeated/ongoing taking, which does not fit well here
• я беру зонтик = present tense, usually I’m taking an umbrella or I take an umbrella

Because зонтик is the direct object of возьму, so it is in the accusative case.

But зонтик is:

• masculine
• singular
• inanimate

For inanimate masculine nouns, the accusative usually looks the same as the nominative.

So:

• nominative: зонтик
• accusative: зонтик

If it were animate, the accusative would usually match the genitive instead.

Historically, зонтик is a diminutive form, so it can suggest a smaller or more familiar umbrella. But in modern everyday Russian, зонтик is very commonly used for just umbrella in general.

So both are possible:

• зонт = umbrella
• зонтик = umbrella, often a bit more conversational or friendly-sounding

In many everyday contexts, зонтик does not strongly imply that the umbrella is tiny.

Yes, absolutely. That version is very natural too, and many learners may even find it easier because высокая вероятность дождя stays together as one phrase.

Compare:

• Вероятность дождя сегодня высокая, поэтому я возьму зонтик.
• Сегодня высокая вероятность дождя, поэтому я возьму зонтик.

Both are correct. The second one may sound a little smoother in many contexts.

No. Я возьму зонтик already sounds complete and natural.

If you say я возьму с собой зонтик, it means I’ll take an umbrella with me, which is a bit more explicit.

So:

• я возьму зонтик = natural, normal
• я возьму с собой зонтик = also natural, but more specific

It is correct and natural, but it sounds a little more formal or analytical than some everyday alternatives.

Common alternatives include:

• Сегодня, наверное, будет дождь. = It will probably rain today.
• Похоже, сегодня будет дождь. = It looks like it will rain today.
• Есть высокая вероятность дождя сегодня. = correct, but less elegant here
• Сегодня высокая вероятность дождя. = very natural

So the original sentence is good, but in casual speech Russians might often choose a simpler way to express the same idea.