Activity for Chgg Clou
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Question | — |
Without trial and error, how can I effortlessly deduce all $n, k_i ∈ ℕ ∋ \binom n {k_1, k_2, ..., k_n} =$ given c? With online or computer software, for a given $c ∈ ℕ $, how can I efficiently deduce all natural numbers that $n, ki ∈ ℕ ∋ \dbinom n { k1, k2, ..., ki} = c$ ? For example below, $i = 1, \color{limegreen}{c = 4,072,530}$. Rule out trial and error! Context >You get two sets of six numbers from 1... (more) |
— | 8 months ago |
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How to decide whether to buy a lottery with a too negative EV, but passable $\Pr($you win jackpot at least once│n plays)? Daily Keno's too negative Expected Value looks scammy. As many play the same lottery repeatedly, I shall consider $\Pr($ you win jackpot at least once│n plays) $= 1 - (1 - p)^n$. But some rational players can sensibly tolerate Keno's fairish $\Pr($ you win jackpot at least once │n plays). Be... (more) |
— | 9 months ago |
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Why do the Expected Values differ, for different wagers of the same lottery? For all the different wagers of Daily Keno's $10 PICK, the odds of winning jackpot are alike : 1 in 2,147,181. Then I calculated their EV. | Wager | Jackpot | EV $= [(Jackpot - Wager) \times Probability] - Wager$ | |:-:|:-:|:-:| | $10 | $2.5m | $\frac{2.5E6 - 10}{2147181} - 10 = -8.84$ ... (more) |
— | 9 months ago |
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How to compare lotteries, when one has highest probability of winning the jackpot, but another the highest Expected Value? Postulate that I shall always pick the lump sum for Daily Grand. The data below showcases that Pr(Keno's jackpot) > Pr(Grand's jackpot) > Pr(Lotto 649's jackpot). $\color{red}{\text{This probability inequality tips you to buy Keno!}}$ But the Expected Values of 1 Lotto 649 play= $= \dfrac{$5E... (more) |
— | 11 months ago |
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How to intuit P(win the same lottery twice) $= p^{2}$ vs. P(win the same lottery twice | you won the lottery once) $= p$? Each lottery draw is independent, with probability $0 “If someone already wins the lottery, then the chance that the person wins the lottery a second time will be exactly the same as the probability they win the lottery if they had not previously won the lottery before,” Harvard statistics professor ... (more) |
— | 12 months ago |
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How can disabled users not be scorned for their disabilities? My mental and physical disabilities (like Memory Disorder) appear to have unnerved some people, and been misconstrued. I apologize. I shall try to improve. But how can I convey my disabilities, so that I am not loathed? Does Codidact offer disability accommodations? Does Codidact want disable... (more) |
— | about 1 year ago |
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Why does $ sometimes render as dollar sign successfully, but other times require escaping? I used solely `$` to write the dollar sign at https://math.codidact.com/posts/288038. As you can see, the `$` rendered the dollar sign perfectly under the heading GOLD BALL DRAW. But under GOLD BALL JACKPOT DRAW, some `$` failed to render as a dollar sign, while some $ did. On the same post,... (more) |
— | about 1 year ago |
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What's mathematically fallacious with Edvin Hiltner's Lotterycodex patterns, to maximize your chance of winning lotteries? I distrust Edvin Hiltner's guidance, but for skepticism unrelated to math. 1. This website is asking for payment in USD for its "patterns". Buyer beware! A fool and his money are soon parted. If this alleged gambit worked, then 2. many more lottery players would tout it. Lotteries would foil i... (more) |
— | about 1 year ago |
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How do I compare lotteries' chances of winning jackpot, when they differ in the maximum number of plays? >[However, there is one way to boost your chances of winning the lottery, says [Dr. Mark] Glickman: Your odds do improve by buying more tickets for each game.](https://www.cnbc.com/2019/05/31/harvard-prof-on-odds-of-winning-multiple-lotteries-like-these-people.html) 1. Do the odds below factor in... (more) |
— | about 1 year ago |
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If a changes to b, then doesn't a + d = b? Why a(1 + d) = b? My 9 year old does not grok DanielWainfleet's answer. How can we intuit why percent change divides the difference by the original number, NOT the new number? >If a changes to b then $\color{red}{a(1+d)=b}$ so $d=(b/a)−1=(b−a)/a$. Why $\color{red}{a(1+d)=b}$? Why can't this be $\color{limegreen}... (more) |
— | about 1 year ago |
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How can school children intuit why over 100, D is larger? But under 100, D% is larger? I can prove the Rule of 100 algebraically, below. But my school kids are hankering after intuition, and a plainer explanation. > > > ## Follow the Rule of 100 > > Should discounts be percentages or absolutes? > > Consider a \\$150 blender. Should you o... (more) |
— | about 1 year ago |
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At what jackpot minimum is playing Lottario rational?  I screenshot https://www.playsmart.ca/social-hub/ironing-out-lottery-odds. >The Main Jackpot: Starts at $250,000 and grows until it’s won. There is no capped maximum amount to the jackpot. >Two chances to win per \\$1 play... (more) |
— | about 1 year ago |
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Isn't Ontario 49 always worse than Daily Grand?  The table above fails to disclose that Daily Grand's top prize is >Annuity of \$1,000 a day for life or a single lump sum cash payment of \$7,000,000 [emphasis mine]. Doesn't Daily Grand's - more moneyed lump sum (\$7M >... (more) |
— | about 1 year ago |
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How can 3/1 ≡ 1/(1/3), when left side features merely integers, but right side features a repetend? On one hand, I know that algebraically, $\dfrac{3}1 ≡ \dfrac{1}{\color{red}{1/3}}$. On the other hand, they differ in practice, not least because $\color{red}{1/3}$ contains 3 as the repetend. For example, if a scrap of physical material must have a 3:1 ratio and a length of 3 m, then I shall mak... (more) |
— | over 1 year ago |
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Isn't "any, some, or all" redundant? Why not write just "any"? Please see the title of this post. In the following quotations, what changes — if anything — if you replace "any, some[,] or all" with just "`any`"? Don't these authors need just "`any`"? I deliberately picked books written by mathematicians, because math requires logic and precision. 9. Yve... (more) |
— | almost 2 years ago |
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How to deduce which ETF is redundant? a of ETF1's holdings in ETF3, a of ETF2 in ETF3, b of ETF1 are in ETF2, b of ETF2 in ETF1. According to https://www.etfrc.com/funds/overlap.php, 1. 47.2% of FIW's 37 holdings $\in$ AQWA's 38 holdings. 2. 47.2% of PHO's 36 holdings $\in$ AQWA. 3. 77.8% FIW's holdings $\in$ PHO. 4. 77.8% PHO's holdings $\in$ FIW. My two goals. I must 5. buy $\ge 1$ Water ETF, such as the 3 a... (more) |
— | over 2 years ago |
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How can you analogize mathematical induction to dominoes falling, if some domino can fail to topple? This analogy doesn't convince me, because what if some domino (after b, the base case) fails to topple? In real life, a domino can remain standing upright if it got placed too far apart from the previous domino — or if the previous domino didn't hit this steadfast domino with sufficient force (to top... (more) |
— | over 2 years ago |
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Is Mathematical Induction truly "induction", or misnamed? By induction, I mean this screenshot from this Youtube video  Abduction as an Aspect of Retroduction | Chiasson, Phyllis | Commens > Induction: > The prefix “in,” also from the Latin has to do with inclusion. Thus, the prefix “in” (to include) combi... (more) |
— | over 2 years ago |
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Why must percent change divide the difference by the old, NOT new, value?  My 14 year old still cannot intuit why the denominator must be the old number, not the new — not even after reading the answers on Math SE. Can someone explain this better? (more) |
— | over 2 years ago |
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Intuitively, why can $a, b$ cycle in ${\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}$? I'm NOT asking about algebra behind $ab = c \iff {\color{red}{b}} = \frac c{\color{red}{a}} \iff {\color{red}{a}} = \frac c{\color{red}{b}}.$ 1. Rather, what's the intuition why $\color{red}{a, b}$ can swap places, whilst c remains in the numerator? 2. What's this phenomenon or behavior calle... (more) |
— | over 2 years ago |
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How can Cross Multiplication be intuited or pictured? average(average(a,b),c) vs. average(a,average(b,c)). Why were my two questions closed? Moderator Peter Taylor's comments feel dissimulating. >I can't even guess at what you're asking. But another user r understood my question. >If the question is "Why does dividing two equal things by the same thing give two equal things" then I'm not sure why... (more) |
— | over 2 years ago |
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How can Cross Multiplication be intuited or pictured? Image alt text I already know, I'm NOT asking about, the algebra. It's NOT intuitive why 3 pears x 4 tangelos = 6 quinces x 2 riberries $\iff$ 3 pears/6 quinces = 2 riberries/4 tangelos. I stumbled the picture below, but how does it proffer intuition?  |
— | over 2 years ago |
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Without trial and error, average(average(a,b),c) vs. average(a,average(b,c)). EXCLUDE Trial and Error. If $a = b = c = 0$, then obviously both sides are equal. My child is 14 y.o. We prefer pretty proofs by picture (but beware), AND intuition! Recondite algebra is not required. But how do I systematically deduce when $\overline{\overline{a, b}, c} = \frac{a}{4}+ \frac{b}{... (more) |
— | over 2 years ago |
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How does counting E twice explain the discrepancy between the third between C and E, third between E and G v. fifth between C and G? I still don't grasp the "source of the discrepancy". "the E got counted twice when we went C,D,E and then E,F,G, but only got counted once when we went C,D,E,F,G." — So what? How does this expound the discrepancy? Impaled on a Fencepost | > The music theorists of the Middle Ages committed a fe... (more) |
— | over 2 years ago |
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How can I intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(b - a)}{{\color{red}{-}}(d - c)} \equiv \dfrac{b - a}{d - c}$? I'm not asking about algebra here which I can effortlessly effectuate. If helpful, let's intuit subtraction as facing backward, and the negative sign as backward steps. How does this intuition assist us to intuit $\dfrac{a - b}{c - d} \equiv \dfrac{{\color{red}{-}}(b - a)}{{\color{red}{-}}(d - c)} \e... (more) |
— | over 2 years ago |
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Why so many books on introduction or bridges to proofs for undergraduates? The two quotes that I embolded below substantiate there are too many books that allegedly assist undergraduates to transition to proofs. If these authors and publishers are desperate for income, wouldn't they profit more from writing solutions (like John Weatherwax Ph.D. (MIT)) to books that don't ... (more) |
— | almost 3 years ago |
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How can Abraham Wald's approach lead you to ignore crucial features of a problem? 1. Kindly see the red sentence below. What exactly does "that approach" mean? I don't know the term for "he peered right through to the mathematical struts and nails holding the story together"? 2. How exactly does Wald's approach $\color{red}{\text{"lead you to ignore features of the problem that... (more) |
— | almost 3 years ago |
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How does Pr(an event next year) $= 1/100$ imply Pr(at least one of these events occurring in the next 25 years) $> 1/5$? Please see the embolden phrase below. It appears to equalize, or at least relate, Pr(an event next year) $= 1/100$, with Pr(at least one of these events occurring in the next 25 years) $> 1/5$? But the former is an equality, whilst the latter an inequality? > Turning to other e... (more) |
— | almost 3 years ago |
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Why isn't $\Pr(diseased|+ test) = \dfrac{\text{number of true positives}}{\text{number of false positives}}$? 1. Technically, the $\color{red}{10}$ quoted below should be 9.99, because $1% \times 999 = 9.99%$. Anyways, why $\Pr(diseased|+ test) = \dfrac{1 \text{ true positive}}{9.9 \text{ false positives} + \color{limegreen}{1 \text{ true positive}}}$? Why isn't $\Pr(diseased|+ test) = \dfrac{1 \text{ t... (more) |
— | almost 3 years ago |
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What does "individuals discount the future in a constant manner" mean? 1. Is the embold phrase referring to Present Value? 2. But how does Present Value relate to the example below with the "online bookstore"? >### AMBIGUITY AND THE FUTURE >Up to now, I’ve said little about how timing affects our reaction to uncertainty. For many decision problems we do not kn... (more) |
— | almost 3 years ago |
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How's the outcome of airplane crashes almost always certain, but the probability is not? Please see the bolden phrase and Table 12.1 below. For plane crashes, did the author mix up which (probability or outcome) is ambiguous, and which is precise? 1. Isn't the outcome of airplane crashes AMBIGUOUS? Because they aren't fatal? But the author wrote "almost always certain". And in Tab... (more) |
— | almost 3 years ago |
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If money's less valuable in the two-bullet case of the Russian Roulette problem, then ought you pay more to remove a bullet when the gun has $\ge 2$ bullets? The emboldened sentences feel contradictory. On one hand, "they are equal reductions in the probability of death". On the other, "money is less valuable in the two-bullet case since they are 1/6 likely to die anyway". What does this imply for the two-bullet case? Ouoght you pay more to remove a bulle... (more) |
— | almost 3 years ago |
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Why should the near-zero prior probability, of 9/11/2001 attacks on the World Trade Centre, overwhelm any subsequent response that may have lowered the objective risk? Can you please expound the embold phrase below? Can this be calculated? > It is notoriously difficult, however, to assess what one’s prior assessment of the risk would have been had one thought of the event before it actually occurred. Most Americans had never contemplated th... (more) |
— | almost 3 years ago |
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Why paradoxical to accept \$3, and avoid betting on Dushanbe's temperature for a prize of \$10? If you don't know Dushanbe's past or historical temperatures, then isn't it rational to accept the $3 for sure? It doesn't feel rational to bet whether the temperature's low or high in Dushanbe, when you have no clue which side is more probable. I don't understand why there's a paradox. If you kn... (more) |
— | almost 3 years ago |
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Why's the unique sub-game perfect equilibrium, that the first player should offer around $1.25 to player 2? Please see the bolden phrase below. Let's abbreviate player $j$ to $Pj$. Even if this is the unique sub-game perfect equilibrium, it feels unnecessarily risky and irrational to me. Why wouldn't you simply offer $2.5 (50% of 5) to P2? You don't know if P2 is rational, reasonable, or sane. I can't ... (more) |
— | almost 3 years ago |
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Why rational to be indifferent between two urns, when urn A has 50-50 red and white balls, but you don't know urn B's ratio? Please see the embolden sentence below. Assume that I'm risk adverse and "prefer the known chance over the unknown". Why's it irrational for me to choose A? > Also, there were problems on the probability side. One famous debate concerned a paradox posed by Daniel Ellsberg (of l... (more) |
— | almost 3 years ago |
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Why are you permitted to define $1 − 1 + 1 − 1 + . . .$? Please see the embold phrase below. Why doesn't $1 − 1 + 1 − 1 + . . .$ possess an intrinsic, Platonic objective meaning? The best way to showcase my confusion, is to burlesque the Riemann Hypothesis. If Hardy and humans can simply define $1 − 1 + 1 − 1 + . . .$, why not just define $\zeta(s)=\sum{... (more) |
— | almost 3 years ago |
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What was Justice Scalia's mathematical mistake in Penry v. Lynaugh (1989)? Please see the bolden phrase below. Please don't hesitate to reduce the amount of quotation, which I know is lengthy, whilst preserving enough context. > But even granting this point, Scalia writes, state legislatures have not demonstrated a national consensus against executi... (more) |
— | almost 3 years ago |
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Why mustn't the proportion of smokers among married people be the same as the proportion of smokers in the whole population? Please see the embolded phrase below. When I read this for the first time, I didn't see this problem at all, and this problem didn't present itself immediately to me. After rereading this four times, I still don't understand this immediate problem! > If you multiply both sides ... (more) |
— | almost 3 years ago |
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How to intuit : married smokers × all people < all smokers × all married people ? How can I intuit inequality (3) in my previous post? The author intuits inequalities (1) and (2), but not (3). Scilicet, how can you explain inequality (3) to a 10 year old? I can't intuit the meaning of multiplying smokers $\times$ people! > If you multiply both sides of ... (more) |
— | almost 3 years ago |
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How to quantify "married people are less likely than the average person to smoke", "smokers are less likely than the average person to be married"? When I first saw inequalities (1) and (2) below, I quantified them as: $\color{red}{\text{1.1. married people When you’re comparing two binary variables, correlation takes on a particularly simple form. To say that marital status and smoking status are negatively correlated,... (more) |
— | almost 3 years ago |
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Why do 3D mental pictures usually suffice for high-dimensional geometry? Kindly see the embolded phrases below. The author doesn't expound why the 3D "mental pictures" are "usually enough". Scilicet, why doesn't "this impoverished vision" hinder high-dimensional geometry, or at least deprive or forestall you from learning all about it? > In the sam... (more) |
— | almost 3 years ago |
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How can you foretell if a problem is one whose solution admits a simple mathematical description? Kindly see the emboldened phrase below. What kind of problems is the author referring to? >### THE UNREASONABLE EFFECTIVENESS OF CLASSICAL GEOMETRY > For Apollonius and the Greek geometers, ellipses were conic sections: surfaces obtained by slicing a cone along a plane. ... (more) |
— | almost 3 years ago |
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If a repair on a vessel costs $2$ and fully repaired vessel is worth $1$, don't we need know worth of broken vessel to decide whether to repair? I divided all prices by 100,000 to simplify the question. The book beneath doesn't stipulate the current value of the vessel. But don't we need to know it, to calculate if it's worth repairing? How do we prove that regardless of the vessel's current cost, the vessel not worth repair? McKendrick. ... (more) |
— | about 3 years ago |
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What kind of logic does “Logic in the Theory and Practice of Lawmaking” employ? I stumbled on 2016 Springer book Logic in the Theory and Practice of Lawmaking. I was curious and leafed through. >  1. What kind of logic is this? I scanned just the pages with the most logic symbols. 2. What level and s... (more) |
— | about 3 years ago |
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In "if and only if" proofs, why's 1 direction easier to prove than the other? This list on Math StackExchange instantiates (biconditional) logical equivalences where one direction can be proved swimmingly, but the other direction is racking to prove. If two propositions are equivalent, why can't they be proved with the same level of difficulty? Please don't troll with frivo... (more) |
— | about 3 years ago |
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Intuitively, why's X% of Y = Y% of X? I didn't spot this trick until I read this: >LPT: X percent of Y is equal to Y percent of X. > I know that multiplication is commutative. Indubitably, $\dfrac{X}{100}Y= X\dfrac{Y}{100}$ But this algebra doesn't betray the intuition! How can this be intuited? (more) |
— | about 3 years ago |
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How to visualize division as splitting Dividend into B equal “partial groups”, then rounding up A partial groups to get a full group? Because $10 \div \dfrac{4}{3}$ isn't an integer, I changed the numbers in this Reddit post. My $X = 6, A = 2, B = 3$. Undoubtedly, I know $6 \div \dfrac{2}{3} = 6 \times \dfrac{3}{2} = 9$, but don't use $\dfrac{a}{b} \div \dfrac{c}{d} \equiv \dfrac{a}{b} \times \dfrac{d}{c}$ here to explain. > ... (more) |
— | about 3 years ago |
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How can I visualize dividing by a fraction as partial and full groups? I can't visualize all these "full groups" and "partial groups." Can someone please picture them? Please see my questions red in-line. Please don't use the identity that $\dfrac{a}{b} \div \dfrac{c}{d} \equiv \dfrac{a}{b} \times \dfrac{d}{c} $. Because $10 ÷ 4/3$ isn't an integer, I changed the num... (more) |
— | about 3 years ago |
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How can I visualize this Compound Interest Chart with indefinite integrals? How can I visualize the integrals below? Can someone draw on the chart and point to where $\int 1 \, dx = x$, $\int x \, dx = \frac 12 x^2 $, ... are ? I don't know which of these charts are more intuitive, and I'll copy and paste two. Is this called a Bar Chart? ![enter image description here][1]... (more) |
— | about 3 years ago |