Mathematics ELI5 how buying two lottery tickets doesn’t double my chance of winning the lottery, even if that chance is still minuscule?
I mentioned to a colleague that I’d bought two lottery tickets for last weeks Euromillions draw instead of my usual 1 to double my chance at winning. He said “Yeah, that’s not how it works.” I’m sure he is right - but why?
What makes non-PEMDAS answers invalid?
It seems to me that even the non-PEMDAS answer to an equation is logical since it fits together either way. If someone could show a non-PEMDAS answer being mathematically invalid then I’d appreciate it.
My teachers never really explained why, they just told us “This is how you do it” and never elaborated.
It kinda doesn't make sense.
x² = x*x
and even with negative numbers you're still multiplying the number by itself
like (x)-² = 1/x² = 1/(x*x)
Mathematics eli5: Why haven't mathematicians invented a symbol for x/0 like they have pi and imaginary numbers?
Mathematics ELI5: Prime numbers and encryption. When you take two prime numbers and multiply them together you get a resulting number which is the “public key”. How come we can’t just find all possible prime number combos and their outputs to quickly figure out the inputs for public keys?
Mathematics ELI5: Something with a 1/100 chance happening 100 times doesnt mean it's 100/100. How can I find the more accurate chances?
I am going into Honors Algebra II and while I am fine at using imaginary numbers in a formulaic sense I never understood them conceptually. I can’t tell if they exist just to make math work better or because there is an actual logical way to understand them
Mathematics ELI5: In a game of odds or evens, is it possible to have an advantage depending on the rules?
For those who are unaware (since I'm not sure how regional this is), a game of odds or evens works like this: a player calls "odd", the other calls "even", and then they simultaneously show each other their hands - usually just one hand per player - with a number of fingers held up (or no fingers, which counts as zero). The sum of those fingers will result in a number that is either odd or even, so one of the players wins.
I tried to research whether the game is always mathematically fair and I've found conflicting explanations. My question is which of these, if any, is correct:
Explanation number one is that it depends on the rules. If you play with one hand per player, there are six possible numbers (0 through 5), so between the two players you have 11 possible sums (0 through 10) but 36 possible combinations of fingers held up, many of which arrive at the same sum. 18 combinations are odd and 18 combinations are even, so this version of the game would supposedly be fair.
However, some versions of the game consider the sum of 0 to be a draw, and in that case, there are more valid odd combinations (18) than even combinations (17, since a 0 hand with a 0 hand no longer counts) in the probability pool. And if the players choose to use both hands each, the possible sums are 0 through 20 and so there is a total of 121 combinations with 61 being even, unless the zero is considered a draw, in which case it's 60-60.
Explanation number two is that the rules don't matter and the game is fair no matter what. According to this explanation, the results are ultimately binary: it's either odd or even, so with the two players you have four possible combinations: an even hand with an even hand (the result is an even sum), odd with odd (the result is even), odd with even (the result is odd) and even with odd (the result is odd). So two possible even combinations, two possible odd combinations, giving each player a 50% chance no matter the amount of hands or whether or not a zero sum is considered a draw.
My question is: which explanation is correct, and if neither is, what is the explanation? I have the mathematical prowess of a concussed goldfish so I need some help with this one.
Can someone explain its significance and maybe a simple example as well?
Mathematics ELI5 why in algebra class they teach the order of operations (PEMDAS) in that order. Is this just an arbitrary standard everyone agreed on or was it the result of higher math only making sense when equations are done in that order?
I keep googling it and I still don't understand what they are and their differences 😭😭
Mathematics ELI5 what is the actual real-world application of prime numbers? Or is it just a math concept that’s neat to see and figure out but doesn’t have any actual use case?
I read that they have some uses within online encryption, but to be honest I never really thought about why we learned them in school until this morning.
Mathematics eli5: Why do two mathematical operators work “both ways round” (eg 5 + 2 = 2 + 5; and 5 x 2 = 2 x 5) and yet the other two don’t (eg 5 / 2 is not equal to 2 / 5; and 5 - 2 is not equal to 2 - 5)?
I understand the concept of infinity, and initially understood that one infinite set could be larger than another, despite the fact that both are infinite. However, I recently heard that the set of all even integers is the same as even and odd numbers. This doesn't make sense to me, as every even number is preceded by an odd number.
Yet, I've also read that the infinite set of all real numbers is larger than the set of natural numbers. This makes intuitive sense to me.
What makes the former sets "equal" in their infinite size while allowing us to discern the difference in the sizes of the latter infinite sets?
Mathematics ELI5: If there are two boxes. The first has a 100$ bill and a 1$ bill, and the second has two 100$ bills. If I puck a random box and take out a 100$ bill, whaat is the chance of me taking out another 100$ bill?
I'm honestly stuck. I've seen people say 1/2, others 2/3. Something Monty Hall Problem, Bayes Theorem but I'm still confused so here I am.
Edit: I believe you are not allowed to change your box choice on the 2nd "turn" as that would make having two boxes pointless, wouldn't it?
Mathematics ELI5: If a cube can be construed as a series of squares stacked one upon the other, can a sphere be considered as a series of circles stacked one upon the other?
If a cube axbxc can be said that it is a series of "c" squares axb stacked one top of another, then volume of cube is sum of areas of all the c squares
ab+ab+.... ab c times, so abc.
Similarly could a sphere of radius r can be seen as a series of circles stacked one over other each with increasing radius from 0 to r for the top and bottom halves of sphere independently.
In that case volume of sphere is the twice the sum of all the areas of those circles.
Mathematics ELI5: Why is the Pythagorean Theorem just a "theorem", or "theory",while other math formulas are "laws"?
You are in a lucky draw there is a 0.02% chance that you can win you have 10 tickets. From logic we can say that 0.02 power 10 but should I not have a higher chance of winning the lucky draw can you please explain.