The Talmud in tractate Pesachim 8b gives an interesting example of the tension between trust in God and the natural order of things while simultaneously adding a new aspect to this problem.
Based on the principle “that those who are busy doing a mitzvah (a good deed or fulfilling a commandment) do not get hurt” the Talmud wonders to what extent one should search for chamets (“leaven” which one is forbidden to eat or have in one’s possession on the festival of Passover) Should one even stick one’s hand in a dark hole to determine if there is chametz inside? What if there is a poisonous snake in the hole? Does the rule “that anybody doing a good deed or mitzvah will be saved from any injury” apply? In other words: Is one allowed to take any risk when performing a mitzvah?
The Talmud answers in the negative by stating that one is only allowed to take a risk when injury is unlikely, but where it is likely, it is not permissible. To prove the point, it quotes an example from an incident in the life of Shmuel (Samuel) the prophet. When God commands Shmuel to go and anoint David as the new king of Israel, Shmuel objects and based on his knowledge of the temper of king Shaul says: “How can I go, if Shaul hears this, he will kill me” (2 Shmuel, 16:2). This is a rather strange and irreligious objection. Why should Shmuel be afraid that he would get hurt by King Shaul? Once God has told him to go, what is there to worry about? Would such a commandment not imply that God will look after Shmuel properly? Surprisingly, God responds that Shmuel should take a heifer and say that he came to bring a sacrifice, so that king Shaul should not discover that he also came to anoint David. (Ibid)
This instance clearly shows that it is not only natural order which needs to be taken into account when trusting God but also human behavior. Since king Shaul is known to have a temper and will strongly oppose the appointment of David as the new king, it should not be taken for granted that God would protect Shmuel from any harm at the hands of king Shaul, especially so when Shmuel can protect himself by “natural” means. While it is questionable if one is allowed to lie in such circumstances, it is definitely permissible not to say all of the truth. It is for this reason that God commands Shmuel to take a heifer and actually bring it as a sacrifice, so that he does not have to lie when he meets King Shaul on his way to anoint David. All he does is to keep some information away from him. (See Malbim ad loc) God would have had to protect him by way of a miracle only if there had not have been another way.
Most interesting however is the Talmud’s point of view that when one is involved in a good deed or mitzvah, one does not have to worry about getting injured, as long as it is not highly probable that such injury would occur. One way of looking at this is that as long as the laws of nature are not openly violated one is allowed to trust in God’s protection. A very good example would be a plane flight. Since most planes land safely at their destination and are built in such a way that it is the law of nature which keep the plane in the air, one is allowed to travel in such a plane. No doubt there is always the risk of mechanical problems which themselves are caused by the law of nature. Still one is allowed to take such a trip and pray that such problems will not occur. This means that as long as the laws of nature are not openly violated and it is possible for God “to deal” with the problem without an open miracle but by His personal intervention, it is permissible to enter such a plane. Once it requires an open miracle and henceforth an open violation of the laws of nature, it would be prohibited.
Once one already finds oneself in the plane and a mechanical problem occurs which only an open miracle could prevent happening should one pray but without relying on guarantees.