lean_workbook_plus_76514

⚠️ Retired — specification defect

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

An unbiased coin with heads probability $\frac {3}{4}$ is flipped 5 times. What is the probability of getting exactly 5 heads?

Why this node was retired

The posted statement is

theorem lean_workbook_plus_76514 (p : ℚ) (hp : p = 3 / 4) (n : ℕ) (hn : n = 5) : (p ^ n) * (1 - p) ^ (n - 1) = 0.78125   :=  by sorry

Exactly-five-heads probability was given an extra failure factor and a wrong numeric answer; “unbiased” conflicts with p=3/4.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Say a biased coin has head probability3/4 and five independent flips; the probability of five heads is(3/4)⁵=243/1024. If the coin is unbiased instead, use1/32.

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.