Which of the following sentences contains an independent and dependent clause? question 3 options: the boy likes cookies; the girl likes icecream. once i went hiking with my best friend. billy jo thinks that the sky is blue because the sun paints it each morning. while dreaming, the dog chased a cat down the alleyway to the garbage dump.

There is only one sentence which contains an independent and dependent clause, and that is sentence number 3 - Billy Jo thinks that the sky is blue because the sun paints it each morning.
Here, 'Billy Jo thinks' is the independent clause, and there are two dependent clauses - 'that the sky is blue' and 'because the sun paints it each morning.'
1 is incorrect because there are two independent clauses; 2 is incorrect because there is one independent clause; 4 is incorrect because there is also one independent clause (while dreaming is a phrase, it is not a clause).