Defined model

Pick one particular grain from a beach

Probability:
4.71 × 10⁻¹⁴%
Odds:
1 to (2.12 × 10¹⁵)
dBan
−153.3 dBan

Mark one grain on the modelled beach, mix every grain, then pick one: finding the marked grain is a one-in-2.122-quadrillion event.

Calculation

p = 1 in 2.122 × 10¹⁵. N = 1000 × 50 × 1 × 0.60 / ((π/6) × 0.0003³)

Assumptions

The hypothetical beach is 1 km long, 50 m wide, and 1 m deep. The grains are modelled as 0.3 mm spheres with 60% solid packing.

Sources

  1. Geometric example model