Correct spelling


Correct spelling, explanation: likelihood is the correct spelling because it is a noun made by combining word likely and suffix -hood. In case of a word ending with y and a consonant before it, y transforms to i. Therefore likelihood is correct and likelyhood is incorrect. y would remain if there was a vowel before it.

Definition of likelihood:
noun, probability, a state of being likely
The likelihood of him being chosen as the team captain was very high.
If you work hard, the likelihood of success is increasing.

Incorrect spelling


Incorrect spelling, explanation: this form is incorrect, because y at the end of the word transforms to i every time any suffix is added, provided y is preceded by a consonant. Here, l is a consonant, so y becomes i and likelihood is the correct spelling. Likelyhood is incorrect, because y would remain in case of a vowel before y.