Simple Noun Expressions

かいがある

Worth doing
Plain form verb + かいがある
ます Stem + がいがある

甲斐がある (かいがある) is a phrase meaning that something has value. In other words, its worth it.

This expression may also be seen as 価値がある.

This pattern is usually past tense.

• 頑張ったかいがあった
  It was worth trying hard.
  
  
• 教師はやりがいがある仕事だ
  Teaching is a job worth doing. (fulfilling)
  
  
• 彼女の顔を見ると、本当に苦労したかいがあったと思う.
  Looking at her face, I think it was really worth suffering. 
  
  

可能性がある

Possibility

You probably already know this one. 可能性 means “Possibility” and 可能性がある means “there’s a possibility.

• 治療しないと死ぬ可能性がある
  If we don’t treat it, there’s a possibility you might die.
  
  
• 大阪に引っ越す可能性がある
  There’s a possibility of moving to Osaka.
  
  
• 彼ができる可能性がゼロ。
  The possibility of him being able to do it is zero.
  
  

恐れがある

There’s a worry that…

恐れがある is a fancier way of saying 可能性がある, but with negative things.
It is an objective and formal phrase, and tends to be used in news and announcements.

• 大雨による洪水の恐れがある
  There’s a worry of flooding due to the heavy rain.
  
  
• 料理の後にガスを切らないとガス爆発の恐れがある。
  If you don’t turn of the gas after cooking there’s a worry of an explosion.
  
  
• 逃亡した容疑者は武器を持っている恐れがあります.
  There’s a worry that the fleeing suspect has a weapon. 
  
  

いわゆる

What is called…/Often called
いわゆる + Noun
Noun + と + いわゆる

いわゆる is technically an adjective, but I’m including it there.
It just means “So called” or “it is called”. i.e. 言われる.

• 彼はいわゆる「科学の天才」だ。
  He is called a “scientific genius”.
  
  
• カニに似ている生物に進化する傾向はいわゆる「カニ化」だ
  The tendency for creatures to evolve into crabs is called “Crabization” (carcinization)
  
  
• 私の好きな食べ物はピザ、ハンバーガーで、いわゆるアメリカンフード大好きです。(Weblio)
  My favorite foods are pizza and hamburgers so I really like what is called “American food”.