Activity for DNB
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Question | — |
In the Lost Boarding Pass Probability Problem, why couldn't Passengers 2-99 sit in Seats 1 or 100, before Passenger 100 boards? Although Tanae Rao was just a high school graduate when he wrote his solution below, it's the most clear out of the solutions I read. 1. I don't understand the step, that I colored in red. Why must Seats 2-99 be occupied, before Passenger 100 boards the plane? 2. Why couldn't one of Passengers... (more) |
— | almost 3 years ago |
| Question | — |
How can "information about the birth season" bring "at least one is a girl" closer to "a specific one is a girl"? Please see the sentences beside my red highlighted words. I don't understand how "Conditioning on more and more specific information brings the probability closer and closer to $1/2$"? Example $2.2 .7$ (A girl born in winter). A family has two children. Find the probability that both children are... (more) |
— | almost 3 years ago |
| Question | — |
Why isn't the probability of being void in 3 specifi c suits $\frac{1/13}{\dbinom{52}{13}}$? Kindly see the sentence UNDER the red line below. Why isn't the probability being void in 3 specific suits $\frac{1/13}{\dbinom{52}{13}}$? As "the probability of being void in 3 specific suits" means you don't want cards of 3 suits, you desire cards of solely ONE suit. If you remove all cards of any ... (more) |
— | almost 3 years ago |
| Question | — |
If Alice must've have classes on at least 2 days, why do you need the intersection of 3 $A_i^C$'s? Can someone please rectify my MathJax? Please see the red phrase below. 1. The question itself never touts or postulates outright that Alice "must have classes on at least 2 days", which feels like an esoteric deduction. So why must she have classes on at least 2 days? 2. If Alice must've cl... (more) |
— | almost 3 years ago |
| Question | — |
How does the change of variable $\color{red}{r↦n−r}$ transmogrify $\sum\limits_{r=0}^n2^{n-r}\binom{n+r}{n}=2^{2n}$ into $\sum\limits_{k=0}^{n} \frac{\binom{2n-k}{n}}{2^{2n-k}}=1$? I'm unskilled at performing algebra with Capita-sigma notation. This comment by a deleted user alleges that the "change of variables $\color{red}{r↦n−r}$" will transmogrify $\sum\limits{r=0}^n2^{n-r}\binom{n+r}{n}=2^{2n}$ into $\sum\limits{k=0}^{n} \frac{\binom{2n-k}{n}}{2^{2n-k}}=1$. I got stuck.... (more) |
— | almost 3 years ago |
| Question | — |
If A & B are joint, can Arby recoup some of his loss only when $P_{Arby}(A \cup B) < P_{Arby}(A) + P_{Arby}(B)$? 1. Please see the sentence alongside the red line below, but the authors didn't write this sentence for the first case ( $P{Arby}(A \cup B) < P{Arby}(A) + P{Arby}(B)$). Thus if A & B ARE joint, can Arby recoup some of his loss in this first class? 2. If I'm correct above, then why do these 2 cases... (more) |
— | almost 3 years ago |
| Question | — |
$\sum_{k=0}^{n} \binom{n}{k}=2^{n} \overset{?}{\iff} \sum_{k=0}^{n} \binom{2n+1}{k}=2^{2n}$ Jack D'Aurizio narratively proved $\color{red}{\sum\limits{k=0}^{n} \binom{2n+1}{k}=2^{2n}}$. Is this red equation related, and can it be transmogrified, to $\color{limegreen}{\sum\limits{k=0}^{n} \binom{n}{k}=2^{n}}$? I started my attempt by substituting $n = m/2$, because the RHS of the green... (more) |
— | almost 3 years ago |
| Question | — |
Why $\color{red}{k\dbinom{k}{1}} \neq$ "first choose the k team members and then choose one of time to be captain"? Because you "first choose the k team members and then choose one of time to be captain", shouldn’t the RHS be $\color{red}{k\dbinom{k}{1}}$? The captain is chosen from the $k$ team members already chosen. $\color{forestgreen}{k\dbinom{n}{k}}$ appears wrong to me, because this means that you're c... (more) |
— | almost 3 years ago |
| Question | — |
Why shouldn't the Bose-Einstein value be used to calculate birthday probabilities? Can you please expound and simplify the embolden phrase below? >As another example, with n = 365 days in a year and k people, how many possible unordered birthday lists are there? For example, for k = 3, we want to count lists like (May 1, March 31, April 11), where all permutations are consid... (more) |
— | almost 3 years ago |
| Question | — |
You're sampling k people from a population of size n one at a time, with replacement and with equal probabilities. Order or not? If you're sampling k people from a population of size n one at a time, with replacement and with equal probabilities, then why does it matter whether your samples are ordered? The quotation below doesn't expound the pros and cons of ordering your samples or not. >1.4.23. The Bose-Einstein result ... (more) |
— | almost 3 years ago |
| Question | — |
What's the bijection between Stars and Bars and Integer Solutions to an Equality? The second quotation below keeps mentioning "bijection", but it never explicitly defines it. So what's the formula for that bijection? A story instead of stars and bars - Making Your Own Sense > On to the third problem. As I said earlier, many people teach students to reduce other problems to ... (more) |
— | almost 3 years ago |
| Question | — |
Are Stars and Bars in Combinatorics related to the Fence Post Error? The bars in the lower picture look like fences. That's why Stars and Bars reminds me of Fence Post Error? >It is common to replace the balls with “stars”, and to call the separators “bars”, yielding the popular name of the technique. We have 5 stars, and 2 bars in our example: > |
— | almost 3 years ago |
| Question | — |
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. Please see the sentence alongside my red line below. Why does part (a) overcount part (b) by a factor of c? 2. Scilicet, why aren't the answers to parts (a) and (b) the same? Whenever you choose a 2-person committee #1, the remaining unchosen 2 members automatically can form the 2-person comm... (more) |
— | almost 3 years ago |
| Question | — |
Explain to a 9 year old — To count each possibility c times, why divide by c? Why not subtract by c? Please see the embolded phrase below. How can you explain to a 9 year old why you 1. must divide by $c$? 2. can't subtract by $c$? >### 1.4.2 Adjusting for overcounting >In many counting problems, it is not easy to directly count each possibility once and only once. If, however, we are... (more) |
— | almost 3 years ago |
| Question | — |
If k = 1, why $n(n-1) \dots \color{red}{(n-k+1)} = n$? Please see the boldened sentence below. I write out the LHS $= n(n-1) \dots (n-[k-3])(n-[k-2])\color{red}{(n-[k-1])}$. Then $LHS| {k = 1} = n(n-1) \dots (n+2)(n+1) \neq n$. >### Theorem 1.4.8 (Sampling without replacement). >Consider n objects and making k choices from them, one at a time wi... (more) |
— | almost 3 years ago |
| Question | — |
Intuitively, if you pick k out of n objects singly without replacement, why's the number of possible outcomes NOT $n(n-1) \dots [(n-(k - 1)]\color{red}{(n - k)}$? I know that $\color{limegreen}{(n-k+1)} \equiv (n - (k - 1))$. But whenever I contemplate choosing k from n objects singly without replacement, I keep muffing the number of possible outcomes as $n(n-1) \dots \color{limegreen}(n-k+1)\color{red}{(n - k)}$. I bungled by adding the unnecessary and wrong ... (more) |
— | almost 3 years ago |
| Question | — |
Why aren't the "21 possibilities here" NOT equally likely? Please see the last sentence below, that I highlighted in red. Example $1.4 .5$ (Ice cream cones). Suppose you are buying an ice cream cone. You can choose whether to have a cake cone or a waffle cone, and whether to have chocolate, vanilla, or strawberry as your flavor. This decision process ca... (more) |
— | almost 3 years ago |
| Question | — |
Without calculations, how can you visualize "that half the squares are white and half are black"? Please see the 2nd para. below alongside my red highlighted words. I can't "[i]magine rotating the chessboard 90 degrees clockwise." I can't visualize how "all the positions that had a white square now contain a black square, and vice versa". Example 1.4.4 (Chessboard). How many squares are t... (more) |
— | almost 3 years ago |
| Question | — |
"A occurred" vs. "something must happen" 1. Why doesn't "Something must happen" mean $s{actual} \in A$? 2. Scilicet, doesn't "A occurs" mean the same thing as "something must happen"? Something must happen. $\iff$ Some event must happen. $\iff$ At least one event must happen $\iff$ Call this event A. Then A occurred.  |
— | almost 3 years ago |
| Question | — |
What story and TWO-digit Natural Numbers best fit Bayes' Theorem chart? Why did Madam Monica Cellio close What story and TWO-digit Natural Numbers best fit Bayes' Theorem chart? as duplicate of What story and ONE-digit Natural Numbers explain Bayes' Theorem chart most simply?? The difference is blindingly obvious. The first question seeks an example of Bayes' Theorem ... (more) |
— | almost 3 years ago |
| Question | — |
What story and two-digit Natural Numbers best fit Bayes' Theorem chart? To complete the table below most comfortably for teenagers, 1. what are the simplest stories? 2. what natural numbers $\le 99$ contrast the base rate fallacy the most? Please don't repeat a number. I'm trying to improve on this question that uses two-digits just $\le 20$, because 3. the... (more) |
— | almost 3 years ago |
| Question | — |
Why isn't \hline rendering here, when it does on Stack Exchange? Please see https://math.codidact.com/posts/280741. I just pasted it on Stack Exchange and my MathJax is rendered perfectly. (more) |
— | about 3 years ago |
| Question | — |
What story and one-digit Natural Numbers explain Bayes' Theorem chart most simply? Some students have sniveled that most examples of Bayes' Theorem use non-integer numbers. I want to try a Bayes' Theorem chart that uses just single digit Natural Numbers $\le 9$. To complete the table below most comfortably for teenagers, 1. what are the simplest stories? 2. what natural numbe... (more) |
— | about 3 years ago |
| Question | — |
How can I deduce which operation removes redundacies? Please don't answer by working backwards from the answer, or by appealing to arithmetic. Act as if you're learning this for the first time. 1. How can I deduce which operation ought fill in the red blank beneath? 2. Why can't it be subtraction? I shortened the original explanation: >Quandary: How... (more) |
— | over 3 years ago |
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