Mathematics - Posts by DNB‭

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Q&A Out of 4 people, why does ways to choose a 2-person committee overcount by 2 the ways to divide the 4 into 2 teams of 2?

1 answer · posted 3y ago by DNB‭ · last activity 3y ago by Tim Pederick‭

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Q&A What's the bijection between Stars and Bars and Integer Solutions to an Equality?

0 answers · posted 3y ago by DNB‭

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Q&A You're sampling k people from a population of size n one at a time, with replacement and with equal probabilities. Order or not?

0 answers · posted 3y ago by DNB‭

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Q&A Which vertical line signifies "putting the cutoff for a positive result at a very low level"?

0 answers · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A How does P(Monty opens door 2) = P(Monty opens door 3), and $P(\text{get car}|M_2)P(M_2) = P(\text{get car}|M_3)P(M_3)$?

0 answers · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A How can I visualize the Law of Total Probability with extra conditioning?

0 answers · posted 3y ago by DNB‭ · edited 3y ago by Wolgwang‭

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Q&A If a 2nd test's independent from the 1st test, then why does $\frac{0.95}{0.05}$ figure twice in $\frac{P(D|T_1)}{P(D^C|T_1)}\frac{P(T_2|D,T_1)}{P(T_2|D^C,T_1)}$?

0 answers · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A Why's the true positive rate termed Sensitivity and true negative rate Specificity, not vice versa? [closed]

0 answers · posted 3y ago by DNB‭ · closed 3y ago by Peter Taylor‭

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Q&A Why aren't the "21 possibilities here" NOT equally likely?

1 answer · posted 3y ago by DNB‭ · edited 3y ago by Wolgwang‭

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Q&A How would you intuit, and soothsay to rewrite, "both girls, ≥ 1 winter girl" as "both girls, ≥ 1 winter child"?

0 answers · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A How do I prove Simpson's Paradox, scilicet $P(A|B) > P(A|B^C)$?

0 answers · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A How can I exploit symmetry to intuit P(A wins) + P(B wins) = 1, without performing algebra?

0 answers · posted 3y ago by DNB‭

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Q&A After $n - 2$ unchosen doors are opened, how does the probability of the $n - 2$ unchosen doors "shift" or "transfer" to the lone unchosen door?

2 answers · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A How do these 3 bell curves of Likelihood, Posterior, Prior pictorialize the Odds form of Bayes' rule?

0 answers · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A Besides guaranteeing 0 ≤ P(A ∩ B) ≤ 1, why can't Independence be defined as P(A ∩ B) = P(A) +,-, or ÷ P(B)?

1 answer · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A In the Lost Boarding Pass Probability Problem, why couldn't Passengers 2-99 sit in Seats 1 or 100, before Passenger 100 boards?

0 answers · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A Why shouldn't the Bose-Einstein value be used to calculate birthday probabilities?

0 answers · posted 3y ago by DNB‭

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Q&A Are Stars and Bars in Combinatorics related to the Fence Post Error?

0 answers · posted 3y ago by DNB‭

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Q&A Explain to a 9 year old — To count each possibility c times, why divide by c? Why not subtract by c?

0 answers · posted 3y ago by DNB‭

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Q&A Intuitively, if you pick k out of n objects singly without replacement, why's the number of possible outcomes NOT $n(n-1) \dots [(n-(k - 1)]\color{red}{(n - k)}$?

1 answer · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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Q&A Without calculations, how can you visualize "that half the squares are white and half are black"?

1 answer · posted 3y ago by DNB‭ · last activity 3y ago by whybecause‭

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Q&A In the Monty Hall problem, why can you just assume the contestant picked door 1? Why are you entitled to relabel the doors, or rewrite this solution with the door numbers permuted?

1 answer · posted 3y ago by DNB‭ · last activity 3y ago by Moshi‭

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Q&A Why "only 1/10,000 men with wives they abuse subsequently murder them" ≠ P(A|G,M) & "50% of husbands who murder their wives abused them” ≠ P(G|A)?

0 answers · posted 3y ago by DNB‭

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Q&A How to intuit that if you destroy someone else's lottery ticket, you didn't deprive her of a chance of winning the lottery?

0 answers · posted 1y ago by DNB‭ · edited 1y ago by DNB‭

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