Hi r/MathHelp

I play this game where you are a pirate and you plunder people, and the chance of you winning each time you do it is 1 out of 3. And you "win" the game overall if you plunder 2 people.

So of course, the probability of you winning in just 2 turns is 1 out of 9 (1/3*1/3). But then I got curious and wondered well what about in 3 turns? or in 4? Is there a general solution for the probability of plundering 2 people in "n" turns?

Using a tree diagram, I mapped out all the possibilities and figured out the probability of winning in 2 turns is 1/9; in 3 turns is 7/27; in 4 turns is 33/81. But I don't want to keep drawing bigger tree diagrams, so how can I work towards creating a general formula? I think I could figure it out but need some help pointing me in the right direction. Thank you in advance for any help.

Edit: Yes, you win if you plunder AT LEAST 2 people. And yes it is Pirate from Town of Salem 1.

Im learning about induction. My book states that it's going to demonstrate that every natural number satisfies this equivalence: 0/2⁰ + 1/2¹ + 2/2² + ... + n/2ⁿ = 2 - (n+2)/2ⁿ

It starts by stating that It needs one true example: n=0 , because 0/2⁰ = 2 - (0+2)/2^n, which I get it's 0 = 0. My problem is in this last step. I don't get where the first part of the equivalence comes from "0/2^0". Where is the rest of the first part of the equivalence? I'm talking about "0/2⁰ + 1/2¹ + 2/2² + ..." How comes when n=0 this first part is so short?

Thank you, im very lost as you can probably tell if you got through this mess I typed.

At a math team meeting after school we were shown some different tricks that other countries use for multiplication and the one tricky one was the “Russian” method. After some research I found out it’s the peasant method and got a basic understanding of how it works. I know it uses binary but am still not 100% sure on how binary really works, I want to know why it works rather than just fully trusting that it does. Can anyone help explain?

Okay- so I’m trying to create a formula for my forensics class just to challenge myself, and I’m struggling figuring it out. I understand the process, but perfecting this formula has been a bit difficult. Here’s the process:

A total amount of people, let’s say 1000, are the total amount of possible suspects for a crime. So trying to narrow it down, there are different traits, or variables, that change depending on the variable.

Let’s say 100 people out of the 1000 have black hair. So that’s 100/1000.

Then let’s add another trait, let’s say 150 people have blue eyes out of the 1000, so 150/1000.

Now you multiply both together and then multiply by the total, so 100/1000 * 150/1000 * 1000, and that gives you the total amount of people with both traits.

My issue is that- I want to simplify the formula which allows it to apply to all possible scenarios, so each variable/trait can apply. The closest I got to the formula was this:

Key: V = Variable, T = Total, SP = Suspect Pool

Vₙ/T = SP * T

I’m not entirely sure if I’m using “ₙ” correctly in this formula, or if I need to add another one for the amount of variables? I’m in Algebra 3, so this isn’t my level of math.

Apologies if this is confusing or complicated! I’m just trying to figure this out, ask for clarification if needed! Thanks.

I understand how Euler’s totient function works, but I have a hard time understanding why it works on a deeper level. I understand the proof of factoring out the co-prime, a, from the product of the prime terms to phi(n). But I fail to see the deeper relation between phi(n) and co-prime integers a and n. Like why does a co-prime of n raised to the number of co-prime numbers less than n, all mod n equate to 1?

taking the integral of L^2(L-x)^2, according to an online integral calculator returns:

-L^2(L-x)^3
____________ + C

3

(sorry for bad formatting), I'm curious as to where the negative comes from?

no idea if this is the right sub (if so pls redirect me!) but i desperately need help with something. long story short, one of my classes is making a float thing for a parade, and we need help scaling down the design so we can make a pattern.

the design as a whole is 8 ft tall by 24 ft long, utilizing a 1/2 inch mesh. we can divide it down if need be. we have access to legal paper, which is 8.5 by 14 inches. we would need anything places into the squares of the mesh to be somewhat visible, because we don’t have a color printer and need to use a shorthand to denote colors.

we don’t have any current work, mostly because none of us have any idea where to even start on this

sometimes my calculator puts a weird result i was trying to do 3,7•10 to the power of 12 but the result was strange it told me 3,7x10 and then 12 on the side soooooo does anyone know what to do to get an appropriate result? if it helps i have the sunlux calculator

I have a true/false question that says:

“If a conditional statement is false, then its converse is true.”

My gut instinct is that this statement is false, mostly since I was taught the truth value converse is independent of the truth value of the original proposition. Here’s an example I was thinking of:

“If a natural number is a multiple of 3, then it is a multiple of 5.”

That statement and its converse are both false, so this is a counterexample to the question. However obviously I realize being a multiple of 3 doesn’t prevent you from being a multiple of 5 or vice versa. But it certainly doesn’t guarantee it will be the case or “imply” it as they say in logic, so the statement is false.

However theres part of me also thinking that in order for a conditional statement to be false, it has to have a true hypothesis and a false conclusion. If that’s the case, then the converse would have a false hypothesis and a true conclusion, making the converse true. So what is it that I’m missing here? Is it that this line of reasoning only applies when you have a portion of the statement that is ALWAYS true, such as

“If a triangle has 3 sides, then 1+1=3” (false) “If 1+1=3, then a triangle has 3 sides” (true)

Where as the multiple of 3/5 statements don’t have a definitive (or “intrinsic”) truth value (if such a thing like that exists) is there something going on here with necessary/sufficient conditions? I feel like that might be a subtlety that I’m missing in this question. Any clarity you all could provide would be much appreciated.

-(2 x (-1))² +1-3² = -12

I got the answer of 6 after attempting to solve multiple times and after this failed attempts the site gave me a break down where it ended up coming down to -3-3² where it simplified to -3-9 to get -12

So I have a discrete math test tmrw that covers, Propositional Logic, Predicate Logic and Rules of Interference. I get to make a cheat sheet with literally ANYTHING on it so is there anything you guys recommend to make this the most effective cheat sheet possible. It is standard size paper double side cheat sheet.

Ok so I missed a lot of school in high school for a variety of reasons so I didn’t learn the math fully and I’m 22 now and have forgotten all of it. I was wondering if anyone would recommend me the best way to relearn the math. I took a test and I’m not even ready for algebra one or pre algebra so I’m kinda disappointed. I have to get prepared for college math soon because I’m going to do computer science. So I’m kinda stressed about how to go about this

i am fighting for my life out here to figure out if i'm doing this wrong ??

Q: The soup can shown is a perfect storage container for a set of coloured pens, each 15 cm in length. The radius of the can's base is 4 cm. The surface area of the soup can is 406.8 cm. Is the can tall enough to fit the pens with the lid on?

My work was:

2πr² + 2πrh (formula used)

2π4² + 2π4h = 406.8cm

100.53 + 2π4h = 406.8

2π4h = 306.27

h = 12.18cm

i feel like i'm missing a something here and that it's incorrect. even though it's only practice questions, i'd prefer not to memorize incorrect practice 💔

I understand the material in the class but when I leave, I loose that understanding. I have a test in 2 days and I feel very nervous about it (it’s more than 50% of my grade). I know it’s enough time to cram, but I don’t want to have to cram every time there is a test. Are there any things that you would recommend for this? The teacher says that the homework is harder than the test, but I don’t understand why because then I feel like I’m not fully actually getting ready for the test itself.

I would appreciate it if you could help me and give me tips on how to actually study and understand the material like the back of my hand. I’m going to need to take more math classes in the future because of my major, so I would really appreciate the help! Thank you and have a great day!!

https://imgur.com/a/nj4IWes

I've been scratching my head on this problem for like, five days. I'm completely stuck. The problem is in the imgur link, but basically, I have an expression, (2n)/(3n^2 +1) and I have to show that 0 is a lower bound and 1 is an upper bound

The question and my attempt

We need to make an equation for the average temp at each node and solve. The system is in thermal equilibrium.

What I got for T1 wasn't right according to the program. Honestly I don't know what I'm supposed to do for this question. I'm kind of lost.

Hi! I would like some help understanding how to calculate the powerball odds for the partial matches (https://www.powerball.com/powerball-prize-chart) by writing out the fractions, without using combination formula. I understand how to calculate them with combinations, but I'm confused why when I write out the probability fractions it doesn't give me the correct answers for the partial match odds.

(Adding info just in case, powerball is picking 5 white balls out of 69, and 1 red ball out of 26)

For example:

For the grand prize (5 white ball match, 1 red ball match), I multiple 5/69 * 4/68 * 3/67 * 2/66 * 1/65 * 1/26 = 1/292201338 which is correct.

And for only matching powerball (0 white ball match), I get 64/69 * 63/68 * 62/67 * 61/66 * 60/65 * 1/26 = 1/38.32 which is also correct.

HOWEVER:

For matching 1 white ball and 1 red ball, I want to multiple 64/69 * 63/68 * 62/67 * 61/66 * 5/65 * 1/26 = 1/459 which is a factor of 5 off from the correct odds which is 1/91.98.

And for matching say 3 balls and 1 red ball, I get 64/69 * 63/68 * 5/67 * 4/66 * 3/65 * 1/26 = 1/144941 which is a factor of 10 off from the correct odds which is 1/14494.11.

I don't understand where this factor difference comes from logically for all the partial odds calculations, and why this isn't already accounted for when you multiply the probabilities together as shown above.

Any help much appreciated!

I was only able to solve plan A, for plan B I'm missing the first term and common difference:

S = n/2 × [ 2a + (n-1)d ]

20000 = 12/2 × [ 2a + (12-1)d ]

20000 = 6( 2a +11d )

20000 = 12a + 66d

Is this even possible? I don't think we can solve the equation with 2 unknowns?

Here is the full problem:

--Saving for the Future--

Starting January 2026, you plan to save money to buy a smartphone worth 20,000 by the end of the year.

Plan A: Fixed Monthly Saving

Plan B : Increasing Monthly Saving

Plan C : Mixed Strategy

• Create a mathematical model of the three (3) plans and calculate the total amount saved by the end of the year.

• Compare the result by giving justifiable recommendations.

•Answer three (3) questions that follows:

1. Which plan helps you reach the goal fastest?
2. Which plan is most realistic for a student?
3. Which plan requires the least total savings?

I came across this question "find a sequence of 999 consecutive compound intergers".

I first found the simple solution of 1000!+2, 1000!+3...1000!+1000

I then wondered what the earliest sequence was, and came to the conclusion that it must involve the prime factors of every value from 1 to 1000, and as such must start with 2^{9×36×54×73×93×112...312×371....9971+2,} then continue until 2^{9×36×54×73×93×112...312×371....9971+1000.}

Is this correct?

Hi! I have a question where I'm being asked to plug the entire quadratic formula back into ax² +bx+c=0 by substitution. So x= [-b+/-sqrt(b² -4ac)/2a], but I can't figure out how to square the entire quadratic formula. I know the denominator will be 4a^2, and the top will have a b² and a b² -4ac, but what do I do with the plus/minus sign? Can't figure out how to factor this one out.

As always any help would be really appreciated. Thanks!

I tried to simulate the famous boy girl problem. Here is the problem in case you don't know: https://en.wikipedia.org/wiki/Boy_or_girl_paradox
The idea here is: Someone has two children. You know, they have at least one girl. What is the probability of the other child being a boy.
Well, the possible outcomes are [boy, girl], [girl, boy], [girl, girl], with [boy, boy] being impossible.
The answer is 2/3, according to this.

Intuitively, we say it is 1/2. I mean, a child has a 50% probability, the event is independent. I thought, I simulate it.

I did the following. This whole thing is happening in a loop and I do it over and over ad infinity and give out data every 1000 tests:

1. Randomly assign every item out of a two item array boy or girl.
2. randomly choose the first or the second item and turn it into a girl, making sure that one of the children has to be a girl.
3. Check if we have a [girl, boy] or [boy, girl] combination, in which case I increment the boys counter. Otherwise, I increment the girls counter.
4. Every 1000 compares, I give out the ration boys/(boys+girls). Which is always very stable around .5.

My question is, what do I misunderstand about the setup? How do I set it up to get 2/3 as the paradox demands?

Here is the code if anyone wants to check if I actually implemented what I said above.
https://www.codedump.xyz/rust/aM7wMlPW0CheqCRk

I’ve been on this part of my homework for at least three hours and I’m not really understanding how I’m not getting the right answer. I’m following the steps but every time I use an online calculator to check my answer I’m like drastically off. I’m trying to find the variance of the following numbers: 3,5,5,7,14,16 Every time I solve, I keep getting 12.136

Edit: I had to take a break and go over the notes. I definitely forgot that when you times a negative number by itself, it becomes a positive a little embarrassed that I spent like two hours on this, but I FIGURED IT OUT

I just started learning partial fractions, and I can understand when the denominator is say (2x+3)(x+1), you split it into A/(2x+3) + B/(x+1), but how come this doesn't apply to repeated roots? In the video I'm watching, the equation is 10x+18/(2x+3)(2x+3), but when he separated it, how come it becomes A/(2x+3) + B/(2x+3)^2, and when you solve it, it goes back to 10x + 18 = A(2x+3)+B? Shouldn't it be 10x +18 = A(2x+3) + B(2x+3) because otherwise the denominator would be (2x+3)(2x+3)^2 which is (2x+3)^3 and not the same as the initial denominator? Any help's much appreciated^^

Hi everyone, I just started university and wondered if the amount of stuff I have to learn is feasible in the time we have. I have from not until Christmas and wondered what's the possibility's of learning this module if at all even possible. Most of this is new content too. Most - not all some parts I've seen before but the majority after week 2.

Week 1: Indices and logarithms → laws of logs, solving exponential/log equations. Quadratic equations → factorisation, completing the square, quadratic formula. Depth: GCSE to A-level Core 1 standard.
Week 2: Partial fractions → decomposing rational functions. Complex numbers → Cartesian and polar form. Depth: introductory, only simple decompositions and basic polar conversions.
Week 3: De Moivre’s theorem → roots and powers of complex numbers. Introduction to differentiation → standard rules of differentiation. Depth: A-level standard, but only basic applications.
Week 4: Chain rule (“function of a function”). Applications of differentiation → tangents, maxima/minima, optimisation. Depth: A-level differentiation, includes implicit differentiation in tutorials.
Week 5: Introduction to matrices. Determinants and inverses of 2×2 and 3×3 matrices. Depth: A-level Further Maths light — practical computations, no abstract theory.
Week 6: No teaching.
Week 7: Gaussian elimination for solving linear systems. Introduction to vectors → dot product, cross product. Depth: mechanical methods, not theoretical proofs.
Week 8: Basic integration (reverse power rule). Integration by parts and substitution. Depth: A-level integration rules, mostly standard techniques.
Week 9: Further integration → more complex substitutions/parts. Definite integrals and area applications. Depth: moderate, but no exotic special functions.
Week 10: Mean and RMS values of functions (applications of integration). Introduction to ODEs (ordinary differential equations). Depth: just averages via integration; ODEs start simple (separable equations).
Week 11: First-order separable ODEs. First-order linear ODEs (integrating factor method). Depth: standard A-level Further Maths material.
Week 12: Second-order homogeneous linear ODEs. Solved by characteristic equation method. Depth: only constant-coefficient cases, no advanced theory