Learners of Japanese are generally more familiar with tabun, another word that expresses possibility or probability. tabun is much more likely to appear in textbooks for Japanese language learners than is osoraku.
However, if you want to add an extra level of sophistication to your Japanese, it pays to know how to use tabun and osoraku because, while there is overlap between them, many situations will call for tabun and not osoraku.
The first thing we'll look at when differentiating these two words is the kanji that forms them. tabun is made up of 多 (ta) meaning "a lot, many, a great number/quantity" and 分 (bun) which means "part(s)." If you take "parts" as meaning parts per hundred, or the familiar idea of percentage, then tabun means "a high percentage," i.e., a good chance, a high probability, a better than average likelihood. In other words, tabun expresses a purely mathematical concept.
osoraku on the other hand is a completely different animal in terms of the kanji character it's based on. If tabun is your bespectacled math teacher, osoraku is a monster, the kanji 恐 (onyomi: kyo) standing for fear, dread and awe, usually expressed in the kunyomi adjective osorashii (terrible, dreadful, terrifying, frightening). However, in solving the puzzle of how and why this scary word is used to express something as everyday as probability, an English analogy readily comes to the rescue: the way we sometimes use "fear" in English, as in "I fear we'll never see him again."
"We'll probably never see him again" (たぶん再開することがないでしょう。 Tabun saikai suru koto ga nai desho）is a flat statement of probability, whereas "I fear we'll never see him again" (おそらく再開することがないでしょう。 Osoraku saikai suru koto ga nai desho）carries a clear emotional message of regret at probably never meeting again.
osoraku should therefore be used only in situations where the probability being expressed is unpalatable, undesirable, regrettable. Whereas tabun has a broader reach and can cover any possibility, desirable or undesirable.
Therefore, for example, when looking at old photos: "That's probably Mary." would be "Tabun Mary da." No one will think twice if you say "Osoraku Mary da," but tabun is better here.
Similarly if you're looking for the family dog: "He probably went that way." "Tabun achi itta daro." is better, but "Osoraku achi itta daro" is also okay.
However, you shouldn't use osoraku when the probable result is desirable. "Tabun kekkon suru daro" (They'll probably get married.) is a neutral expression of probability, but if you were to say "Osoraku kekkon suru daro" it would indicate that the likely prospect of those two getting married sends shivers up your spine.
To sum up, feel free to use tabun for any probability; it is completely neutral and covers all bases. However, exercise a little caution with osoraku and use it only when the possibility being expressed is one you'd rather not happen.
Now try the following osoraku test. Which sentences can use "osoraku"? (Answers below.)
1. Ashita wa ________ ame desho. (It'll possibly rain tomorrow.)
2. Bokutachi wa ________ katsu daro. (We could well win.)
3. ________ ma ni awanai daro. (She may well not make it on time.)
4. ________ nakushita yo. (You probably lost it.)
5. ________ mou yoku natta deshou. (It's probably come right already.)
Tabun can be used in all sentences, but osoraku should be used only in sentences one, three and four.
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