Mathematics - Posts by DNB‭

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Q&A Why's a 2-player game with "win by two" rule = Gambler's Ruin where each player starts with $2? Why N = 4?

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

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Q&A If A & B are joint, can Arby recoup some of his loss only when $P_{Arby}(A \cup B) < P_{Arby}(A) + P_{Arby}(B)$?

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

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Q&A How do you calculate $P(X = n|G), P(X = n|G^C)$ by 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 How to vaticinate calculating $w_{k + 1} = w_1(1 + \dfrac{1- p}{p} + \dots + [\dfrac{1- p}{p}]^k)$ separately for $p = 1 - p$ and $p \neq 1 - p$?

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

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Q&A How can a 15 year old construe the LHS of Generalized Vandermonde's Identity, when it lacks summation limits and a summation index?

2 answers · posted 3y ago by DNB‭ · last activity 3y ago by r~~‭

Question summation

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Q&A Can the bijection for the Lost Boarding Pass Probability Problem, be formulated or pictured?

1 answer · posted 3y ago by DNB‭ · last activity 3y ago by r~~‭

Question combinatorics

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Q&A If C = Calvin wins the match, and $X \thicksim Bin(2, p) =$ how many of the first 2 games he wins — then why P(C|X = 1) = P(C)?

1 answer · posted 3y ago by DNB‭ · last activity 3y ago by Peter Taylor‭

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Q&A To correct for overcounting, why can't we divide by the sum of the over-counts? [duplicate]

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

Question combinatorics

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Q&A How can "information about the birth season" bring "at least one is a girl" closer to "a specific one is a girl"?

1 answer · posted 3y ago by DNB‭ · last activity 3y ago by r~~‭

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Q&A What's wrong with evaluating $n(n-1) \dots (n-[k-3])(n-[k-2])\color{red}{(n-[k-1])}$ at $k = 1$?

1 answer · posted 3y ago by DNB‭ · edited 2y ago by Peter Taylor‭

Question notation

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Q&A Why 1. multiply the number of independent options? 2. add the number of exclusive options?

3 answers · posted 3y ago by DNB‭ · last activity 3y ago by Tim Pederick‭

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Q&A Intuitively, why does $p$ vary inversely with $P(C_3 \mid D_2)$? But directly with $P(C_2 \mid D_3)$?

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

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Q&A How can you "easily see that such squares [of side length $\sqrt{13}$ and $\sqrt{18}$] will not fit into the [4 × 4] grid"?

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

Question geometry

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Q&A How to intuit, construe multiplicands and multiplicators $\le 10$ resulting from $\dbinom pc$, WITHOUT division or factorials? [duplicate]

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

Question combinatorics

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Q&A $g(x)\xrightarrow{x\to\infty}\infty$ Implies $g'(x)\leq g^{1+\varepsilon}(x)$

posted 2y ago by DNB‭ · edited 2y ago by Peter Taylor‭

Answer

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Q&A 25% probability that there was a chance of avoiding injury $\quad$ vs. $\quad$ 25% chance of avoiding injury

2 answers · posted 1y ago by DNB‭ · last activity 1y ago by Hudjefa‭

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Q&A 2 construals "of 100 patients presenting with a lump like the claimant’s in Gregg v Scott, 42 will be ‘cured’ if they are treated immediately."

2 answers · posted 1y ago by DNB‭ · last activity 1y ago by r~~‭

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Q&A Why's Pr(the running total of a fair dice rolled repeatedly = n) = $\frac16 (p_{n-1} + p_{n-2} + p_{n-3} + p_{n-4} + p_{n-5} + p_{n-6})$?

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

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Q&A How to intuit p = Calvin's probability of winning each game independently = $1/2 \implies$ P(Calvin wins the match) = 1/2?

1 answer · posted 3y ago by DNB‭ · last activity 2y ago by viäränlaenen‭

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Q&A What story and two-digit Natural Numbers best fit Bayes' Theorem chart?

0 answers · posted 3y ago by DNB‭ · reopened 3y ago by Monica Cellio‭

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Q&A For (a variation) of the Monty Hall problem, what permits you to repaint doors 2 and 3? What permits you to replace p with $1 - p$?

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

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Q&A Does "both girls, ≥ 1 winter girl" = "both girls, ≥ 1 winter child" let you generalize the problem statement that postulated both children as girls?

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

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Q&A Why isn't the probability of being void in 3 specific suits $\frac{1/13}{\dbinom{52}{13}}$?

0 answers · posted 3y ago by DNB‭

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Q&A If k = 1, why $n(n-1) \dots \color{red}{(n-k+1)} = n$?

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

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Meta What story and TWO-digit Natural Numbers best fit Bayes' Theorem chart?

2 answers · posted 3y ago by DNB‭ · last activity 3y ago by Monica Cellio‭

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Posts by DNB‭