Question

With God's help
Hello Rabbi,
I wanted to ask: if a person prays for some event, and that event then happens, is it correct for him to attribute it to his prayer?
For example, suppose someone prayed to win the lottery and indeed won the lottery. The probability of that event happening is very low. On the other hand, he thinks the probability of it happening given that he prayed is significantly better (the fact is, he prays). Likewise, the probability that there is a God who intervenes in the world is, in his view, not low at all (again, the fact is that he prays). So I think that, using inverse probability in the style of Bayes' formula, somewhat like column 144, the reasonable interpretation from his perspective is that the win really did come because of the prayer.
But when an outside investigator examines things, he knows that 95% of people who fill out lottery tickets probably pray, and over the course of hundreds of years there have been "countless dice rolls" of lottery games, so of course the lottery will fall to a believer at some point, and there is no miracle here.
So who is right with respect to the truth? Seemingly the person is obviously right from his own point of view, but the investigator also seems right.
The same idea can be asked about any everyday event that is a "fluke" and unlikely to occur (as long as we are not talking about a violation of the laws of nature or some other extreme improbability). Such events, even though they are improbable for any one person individually, are bound to happen because there are countless events. On the other hand, one could say that the person's prayer "marks" these events in advance, and if so it gives them an advantage. But still, given that many people pray and therefore many such events are marked, how can one decide whether the prayer caused the event?
For example, at one time you gave the example of getting a ride that stopped for you to Yeruham. If you had prayed for that in advance and it had indeed happened, would it be reasonable to claim that it happened because of the prayer? After all, across all of history there have been countless dice rolls, as it were, and rides are constantly happening. Also, quite a few hitchhikers pray for a ride.
 
I thought about imagining a hundred-sided die rolled a thousand times. Then each face should come up ten times in total over the course of the game. But on each individual roll, the probability of landing on that face is one in a hundred. Therefore, if someone prays that the die should land on that face דווקא on that one particular roll, then one really can speak of an advantage for prayer. But the issue is that believing people are constantly praying and marking, say, 100 of the 1,000 rolls on a regular basis, so the chance that it will land on that face is not bad at all. But then the question arises: what if that person does not pray constantly, but only occasionally, and on that occasion when he prayed it happened? Does the fact that other hitchhikers pray regularly undermine his believing interpretation?