Defined model

A needle in a haystack

Probability:
9.4 × 10⁻⁷%
Odds:
1 to (1.06 × 10⁸)
dBan
−80.3 dBan

Hide the modelled needle inside the hay bale, then choose one point uniformly by volume. Only about one point in 106 million lies inside the needle.

Calculation

p = (0.00069 / 1.25)² × (0.037 / 1.20) ≈ 9.40 × 10⁻⁹ ≈ 1 in 106 million

Assumptions

The calculation converts every dimension to metres. The needle is modelled as a solid cylinder 37 mm long and 0.69 mm wide. The bale is a cylinder 1.25 m in diameter and 1.20 m wide, including its air gaps. The needle lies fully inside. Its tip and eye are ignored. The calculation models a uniformly sampled point rather than a search by hand.

Sources

  1. John James Needle Guide: Sharps size 7 37 mm length and 0.69 mm diameter
  2. New Holland Roll-Bar 125 1.20 m width and 1.25 m diameter