If the orbital plane of a planet and its moon were sufficiently aligned, the moon could cause a solar eclipse every lunar month. What are the odds of that happening? To answer, I would guess that one would need to posit a distribution describing the variance between orbital planes and posit a distribution of distances between the three bodies and a distribution of planet sizes. I suspect that exactly aligned is the most likely and that orbital planes being at right angles would be least likely based only on the prevailing angular momentum of the system, but I could envision some precession or other counter-intuitive phenomenon changing that. As far as the sizes go, to simplify, maybe a moon that's much smaller (does the center of the moon's shadow intersect with the planet) than the planet and a sun that's quite far away.
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2$\begingroup$ Note that our Moon is unusually large relative to the Earth's mass, and its orbital plane is quite close to the ecliptic (inclination ~5.14°). Most Solar System moons tend to have orbital planes close to their primary's equatorial plane. $\endgroup$– PM 2RingCommented Apr 3 at 5:26
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$\begingroup$ I have some info here about eclipses by Triton on Neptune astronomy.stackexchange.com/a/55620/16685 I didn't mention it earlier, because it's a counter-example, but you may find it interesting. ;) $\endgroup$– PM 2RingCommented Apr 3 at 10:01
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$\begingroup$ I don't understand what kind of answer you are looking for. Yes, of course it depends on the relative inclination of the orbital planes, and on the relative solid angles occupied by the moon and the star (which in turn depend on the diameters of the objects and their distances) and on the ecentricity of the orbits and their relative alignments. $\endgroup$– ProfRobCommented Apr 3 at 11:13
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$\begingroup$ @ProfRob It's possible there's an orbital dynamics reason that one would never see aligned orbital planes, but failing that, this seems like a fairly straightforward application of probabilities to arrive at a number on the low side between zero and one. $\endgroup$– user121330Commented Apr 5 at 3:22
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1$\begingroup$ @user121330 let's assume the inclination of the Moon's orbit to the ecliptic was 1 degree, but everything else was the same. Would it cause eclipses every orbit? See what parameters you need to look up to do that calculation, and then think about what probability distributions you want to assume for those parameters (e.g., the probability of being at a given distance from the star or the probability of the moon having a given diameter). Since these (and several others) do not have unique values, then the answer to your question cannot be expressed as a number. $\endgroup$– ProfRobCommented Apr 5 at 6:40
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