# TRAPPIST 1 and planet statistics?

From what I understand, the TRAPPIST 1 system was discovered using the transiting method looking at 20 ultra-cool small stars. I'm not sure how many have been observed since this study.

What I wonder is, what would we expect to see if all 20 had planets? I'm not sure how many planetary systems in this and future similar studies we would expect to see edge on. What about radial velocity measurements?

Did we just get lucky with TRAPPIST 1?

The probability of observing a planet transit is approximately $(R_p + R_s)/a$, where $R_p$ and $R_s$ are the planet and stellar radius respectively and $a$ is the semi-major axis of the planet's orbit. This assumes that planetary orbits are circular and randomly oriented with respect to our line of sight to the star (for which there is little or no counter-evidence).
In the case of Trappist-1, it has an estimated radius of $R_p=0.11R_{\odot}$, the planetary companions have radii and semi-major axes of (in units of Earth radii and au respectively) (1.09,0.011), (1.06, 0.015), (0.77,0.021), (0.92,0.028), (1.05, 0.037), (1.13, 0.045), (0.75, 0.059).