Use Marilyn vos Savant Probabilistic Clarity Prover with your AI.

Validate probabilistic clarity

You must: (1) CHALLENGE INTUITION. state the gut answer, then compute the actual probability. If they agree, show the computation. If they diverge, explain why intuition fails. The Monty Hall problem proved 10,000 PhDs wrong. never trust intuition without math, (2) ACCOUNT FOR BASE RATES. apply Bayes' theorem. State the prior probability before updating with new evidence. A 99% accurate test with 0.1% prevalence yields ~9% posterior, not 99%, (3) SCRUTINIZE SAMPLES. examine size (is it powered for the claimed effect?), selection method (random vs. convenience vs. self-selected), and bias (survivorship, confirmation, selection). "Studies show" without methodology is anecdote, (4) QUESTION FRAMING. check whether the question itself hides options, creates false dichotomies, or anchors the answer. Reframe the question and see if the answer changes, (5) VERIFY INDEPENDENCE. confirm events are actually independent before treating them as such. Test for correlation, seasonality, and hidden common causes. "Each event is independent" must be proven, not assumed. If rejected, fix the specific probabilistic reasoning gap. Structured reflection capability for probabilistic reasoning. forces intuition-vs-computation verification, base rate accounting, sample scrutiny, framing analysis, and independence testing before accepting any data-driven conclusion or risk assessment. Catches Intuition Unchecked (accepting a gut answer without computing the actual probability. the Monty Hall problem: intuition says 50/50, math says 2/3 for switching. 10,000 PhDs wrote to Marilyn vos Savant insisting she was wrong. they trusted intuition over computation. The birthday paradox: 23 people in a room, intuition says ~6% chance of a shared birthday. Actual probability: 50.7%. Human probabilistic intuition is systematically miscalibrated. every gut answer must be checked against actual computation), Base Rate Neglected (ignoring prior probability when evaluating new evidence. a medical test is 99% accurate. A patient tests positive. Intuition: 99% chance of disease. Reality: if the disease prevalence is 1 in 1,000 (base rate 0.1%), the posterior probability is only ~9% (Bayes' theorem: P(disease|+) = 0.001 × 0.99 / (0.001 × 0.99 + 0.999 × 0.01) ≈ 9%). Without the base rate, a 99% accurate test feels like 99% certainty. it is 9%), Sample Unexamined (accepting "studies show" without examining sample size, selection bias, and survivorship. "our users love the product" based on an NPS survey sent to active users. The 67% who churned last quarter were never surveyed. N=47 self-selected respondents is anecdote, not data. A convenience sample from Twitter followers is not representative of your customer base. Survivorship bias: studying successful startups to find patterns ignores the 90% that failed using the same patterns), Framing Accepted (answering the question as asked without questioning whether the question itself is misleading. "Would you rather save 200 people out of 600, or have a 33% chance of saving all 600?" and "Would you rather let 400 people die, or have a 67% chance that all 600 die?". identical outcomes, systematically different choices. The Monty Hall problem's framing hides that your original 1/3 choice never changed. the question makes it feel like a new 50/50 choice. Every question has a frame. the frame shapes the answer), and Independence Assumed (treating correlated events as independent. the gambler's fallacy: assuming a roulette wheel has memory ("it's due for red"). The reverse: assuming sales are independent when they have strong seasonality. A portfolio of "diversified" mortgage-backed securities that all correlate with the same housing market is not diversified. the 2008 financial crisis was, at its core, an independence assumption failure. Correlation ≠ independence, and "each event is independent" must be tested, not assumed). Call once per risk assessment, statistical claim, or data-driven conclusion