How does maximum distance from the ecliptic determine the frequency for which a planet is likely to be occulted by the Moon? Consider that Venus can stray ~7 degrees from the ecliptic and that Jupiter only strays a maximum of ~1.8 degrees from the ecliptic. The Moon strays up to about 5 degrees from the ecliptic. When the Moon passes in front of another body, the body is said to be occulted by the Moon.
Ignoring the planets' apparent diameter and Venus's curious path across the sky as viewed from Earth, for any given pass of Venus or Jupiter by the Moon (i.e. both bodies have the same right ascension), which planet is more likely to be occulted by the Moon?
My intuition tells me that Jupiter would be more likely than Venus to be occulted by the Moon as it is always inside the Moon's possible path. That said, it only occupies a small part of that path and Venus can cover the whole thing, straying outside only a little bit.
Assuming the two planets to be point sources, how would I express each planet's chance of being occulted? Would I just take the percentage of chance that it is inside the Moon's possible path (Jupiter: 100%, Venus: 5/7 = ~70%), then multiply that coefficient by the chance that the Moon's ~0.5 degree diameter will pass over any given spot (say the 0 degree line: ~10%)? That gives Jupiter a 10% chance of being occulted and Venus a 7% chance of being occulted, which according to my years of casual observation is much too optimistic.
 A: Even acknowledging that this is more of an idealized approximation, the orbital inclination of Venus to the ecliptic is about 3.4°, so your figure of 7° seems perhaps an unintentional doubling.  For Jupiter your figure is more realistic, though still overstated (should be more nearly 1.3° rather than 1.8°).
But let's have it both ways by letting the planet's orbital inclination be a parameter $\alpha$.  Assume an observer hypothetically located at the center of (a transparent) Earth, because the Moon with its 0.5° angular diameter is close enough to Earth to cause significant parallax (different viewers will see the Moon in different positions with respect to celestial bodies).
As discussed in the Comments, we assume that the two angles of ecliptic "latitude" (above or below the ecliptic) when the Moon passes the other body (at their common ecliptic "longitude") are independently and uniformly distributed on $[-5°,+5°]$ for the Moon and on $[-\alpha,+\alpha]$ for the planet.
Given this uniform probability density over that rectangle, the chance of occultation would be the fraction of area covered by the strip where Moon's latitude and planet's latitude differ by less than 0.25°.  If $\alpha \le 4.75°$, the portion of overlap between the rectangle and the strip is a parallelogram with area $\alpha$ out of the rectangle's area of $20\alpha$, giving a probability of 5%.  If $\alpha \ge 5.25°$, the portion of overlap is also a parallelogram, one with area $5$ out of the rectangle's area $20\alpha$, giving a probability of $\frac{1}{4}\alpha^{-1}$.  
For the intermediate values of $4.75° \lt \alpha \lt 5.25°$ it might be easiest to think of the overlap as the remnant from removing two congruent isoceles right triangles from the rectangle, leaving $20\alpha - (\alpha + 4.75)^2$ out of $20\alpha$ as the probability of occultation.
