Step 1: What the terms really mean
The Sanskrit term astika is often translated as theist, but in the Indian knowledge tradition the word is tied to the Vedas, not to God. Think of it as a question: does this school treat the Veda as a reliable source of truth?
Step 2: Plan
Sort the four options into two groups. One group is about God or worship. The other group is about the status of the Vedas. The correct option must come from the second group and must be positive.
Step 3: Options 1 and 2 are about God and worship
Option 1 talks about disbelief in God and option 2 talks about idol worship. Neither is the classical criterion. A Mimamsaka can reject a creator God and still be astika, so these cannot be the deciding basis.
Step 4: Options 3 and 4 are about the Vedas
Option 4 says the Vedas are not accepted, which describes the nastika schools like Charvaka, Jaina and Bauddha. Option 3 says the Vedas are accepted, which describes the six astika darshanas.
Step 5: Pick the answer
Since the question asks what decides theism (astika), the answer is the acceptance of the Vedas, which is option 3.
Final Answer:
Acceptance of the Vedas as valid knowledge decides astika, so option 3 is right.
\[ \boxed{3} \]