An example that should show this approach is wrong:
Suppose that the jar contains 500 double-head coins and 500 double-tail coins. You pull a coin from the jar, flip it 10 times, and get 10 heads. What is the probability it will come up heads next time?
OK, so now imagine that there are 1000000 double-headed coins, 1000000 double-tailed coins, and one fair coin. Now (1) there's still (potentially) randomness present, so it's not "completely different" from the original problem, but (2) the ignore-the-data approach gives an obviously wrong answer whereas using the data gives a believable answer.
Suppose that the jar contains 500 double-head coins and 500 double-tail coins. You pull a coin from the jar, flip it 10 times, and get 10 heads. What is the probability it will come up heads next time?