The Ledger That Loves Fives

Honestly recorded amounts have a uniformly random final digit (0 through 9, independently across records). If a ledger has been fabricated, its author favours round numbers, and each record's final digit is 0 or 5 with probability 1/2 each, independently across records. A ledger is fabricated with prior probability $1/5$. An auditor samples two records from one ledger and finds that both end in 0 or 5. What is the posterior probability that the ledger is fabricated? Give a reduced fraction.

• conditional probability
• distributions
• graph theory

Source: Terminal-digit analysis used in forensic accounting and data-integrity checks (cf. Nigrini on digit tests). Statement written for AxiomIQ.