lean_workbook_plus_61095

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

A numbers is selected at random from the set $A={1,2,3,...,180}$ . What is the probability that the selected number is neither divisible by $3$ nor divisible by $5$ ?

Why this node was retired

The posted statement is

theorem lean_workbook_plus_61095 (s : Finset ℕ) (hs : s = (Finset.Icc 1 180)) : (s.filter (λ x => ¬ 3∣x ∧ ¬ 5∣x)).card / s.card = 8 / 15   :=  by sorry

Both cardinals are divided in ℕ, so any proper event subset yields0 and the RHS8/15 is also0.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

For a uniform random integer from1,…,180, count96 integers divisible by neither3 nor5 and prove the real/rational probability96/180=8/15.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.