lean_workbook_plus_79289

⚠️ 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.

The probability that one player receives a pair is $\frac{1}{4}$ . The probability two players receive a pair is $\frac{1}{4} \cdot \frac{1}{3} = \frac{1}{12}$ . The probability that three players receive a pair is $\frac{1}{4} \cdot \frac{1}{3} \cdot \frac{1}{2} = \frac{1}{24}$ . The probability that four players receive a pair is $\frac{1}{4} \cdot \frac{1}{3} \cdot \frac{1}{2} \cdot \frac{1}{1} = \frac{1}{24}$ . The answer is $1-\left(\frac{1}{4}-\frac{1}{12}+\frac{1}{24}-\frac{1}{24}\right) = \boxed{\frac{5}{6}}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_79289 :
  1 - ((1/4) - (1/12) + (1/24) - (1/24)) = 5/6   :=  by sorry

Evaluate the displayed arithmetic identity over ℚ or ℝ. The probability interpretation requires the omitted sample-space assumptions.

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

Proposed corrected statement

Evaluate the displayed arithmetic identity over ℚ or ℝ. The probability interpretation requires the omitted sample-space assumptions.

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.