Option 1 -> improbable means unlikely; this is a synonym of implausible, not an antonym.
Option 2 -> doubtful means questionable or uncertain; this is also a synonym of implausible.
Option 3 -> farfetching (far-fetched) means hard to believe; another synonym of implausible.
Option 4 -> convincing means believable and persuasive; this is the opposite of implausible.
Hence, Option 4: convincing -> IMPLAUSIBLE means not believable or unlikely, while CONVINCING means believable and credible, making them antonyms -> correct