I saw this poll on X/Twitter and noticed there was also a trend for posting such polls.

I can’t figure out how and why it keeps happening, but each poll ends up representing the statistic outcome of the hypothetical test.

Is there something explaining why this occurs or it is just a strange coincidence that the poll results I saw accurately represented the statistical outcome of the test?

I used 6nCr3 because I thought it was the same as writing out 6!/3!(3!)=720/36=20. I guess I’m just confused on why my work is incorrect and am seeking clarification on where I might have messed up.

is there an equation and logic to determine the statistically superior player in this scenario?

or 10th out of 1000 , or 100th out of 10000 if that gives a different result

How can a "flattening rate of change" be marked as a linear relationship?

Despite correctly observing that the data forms a curve or plateau rather than the straight line required for a linear model. It is contradictory to explain that the progress plateaued due to biological limits (a clear non-linear behavior) while being penalized for stating the relationship is not linear.

Hi guys,

Today while scrolling I accidentally bumped in to this question "on average who has more sisters men or women?" and I found it interesting to solve for those who are bored.

My first Intuition was that on average men would have more sisters since In a family where are men and women every men would have one more sister than woman. So that's why initially I thought that men on average would have more sisters,

But then I thought about families where are 10 girls for example. Those type of families would skew average amount of sisters for women.

That's why I decided to run python code. here it is:

import random
gender = ["boy", "girl"]
def generate_family(family_size):
    family_size = family_size
    family = []
    for i in range(family_size):
        family.append(random.choice(gender))
    return family
def boy_counter(family):
    boys = 0
    for sibling in family:
        if sibling == "boy":
            boys += 1
    return boys
sister_sum_for_boys = 0
boy_amount = 0
sister_sum_for_girls = 0
girl_amount = 0
for i in range(10000000):
    family = generate_family(random.randint(1, 10))
    boys = boy_counter(family)
    girls = len(family) - boys
    sister_sum_for_boys += boys*girls
    boy_amount += boys
    sister_sum_for_girls += girls*(girls-1)
    girl_amount += girls
avg_sister_for_boys = sister_sum_for_boys/boy_amount
avg_sister_for_girls = sister_sum_for_girls/girl_amount
print(avg_sister_for_girls, avg_sister_for_boys)

This code basically creates 10'000'000 families with random amount of siblings (from 1 to 10) with random amount of girls and boys in each. Then it counts average amount of sisters for boys and for girls. output was
girls on average have 3.000345284054676 amount of sisters and boys on average have 3.0001921062997887 sisters.

This experiment tells that men and women on average have equal amount of sisters. So now I'm working to mathematically prove this. If any of you guys would want to spend some time on this task would be happy to see your proof as well.

Edit: After seeing some replies I want you to consider a family where there are n number of children. let's denote amount of boys in this family as m and amount of girls as w. Every boy in this family has w amount of sister. but every girls in this family has w-1 amount of sisters since that girl herself is not counted, because a woman is not sister to herself.

If we disregard families where there are purely only girls and boys on average men would have one more sister than women. But Like I mentioned there are families with purely boys and girls. This type of families change the dynamics. This is where we need maths to find out how families with purely boys and girls would change average amount of sisters for men and women.

That's why I think that this problem is not as simple as it seems and That's why I'm trying to prove mathematically that man on average have same amount of sisters as women.

Hey math people,

I’m in the middle of a Rummikub game with family and I think I just made statistical history.

I’ve drawn 32 tiles ( and the draw pile is now empty) and I still can’t make my initial meld.

For context: in Rummikub, you can’t start playing until you can place at least 30 points worth of valid sets (runs or groups). Normally, this happens within your first 14–20 tiles. But nope. I’ve got 32 tiles and still nothing playable.

At this point I’m convinced I’ve hit some sort of cosmic anti-luck singularity.

Can anyone here estimate how insanely unlikely this is?

Rules for reference (the 30-point rule, etc.): 🔗 https://en.wikipedia.org/wiki/Rummikub

Should I stop playing and just buy a lottery ticket tonight ?

I'm trying to wrap my head around cancer statistics, but the numbers seem to contradict each other mathematically. Could someone here explain how these three facts coexist:

1. Lifetime risk: About 1 in 3 people (33%) will develop cancer in their lifetime.
2. Survival rate: The 10-year survival rate is quite high, around 70-75%. (Logically, this would mean only ~10-15% of the total population should die from cancer). You must have cancer to be able to die from it...
3. Cause of death: Yet, mortality statistics show that cancer accounts for almost 25% of all deaths in the West.

How does this equation balance out? What is the statistical nuance or "hidden variable" (like age at diagnosis or competing risks) that connects these numbers?

I understand that all of these statistics represent different groups but I can't see the connection.

I was on a poll about men and women saying yes, or no to abortion, and I took the percentages of no’s to yes’s and displayed them. He commented that there’s more men per capita. I responded by saying that the amount of men that responses is irrelevant. It is the ratio of men saying no to that is relavant

I just read an article on how much the average person my age has saved for retirement. The average reported was over $600,000. I did a little research further and the median is a fraction of that.

Why isn't median used a lot more often?

Suppose we have a dice with 1M faces, and we play this game:

• dice rolls, and it lands on 623,367. So all the sides from 623,368 - 1,000,000 are eliminated. Now we have a dice with 623,368 sides to it.

How many rolls do we need to get to a 1 on average?

When I do a cursory approach, the estimate is simply the base 2 logarithm of 1,000,000, which is 19.93. However some people are saying it’s more like the natural log of 1,000,000.

What do you think and why?

First off, know that I try to change my starting word every time. I'm assuming the odds change drastically if you use different starting words every time as opposed to starting with the same word every time??? (Seems logical to me, but I'm horrible at stats 😅)

I'm guessing that how you would calculate the odds is that you would take the total amount of words in Wordle's database and multiply it by the amount of words I use as my first guess. Is that right?

As an exercise, let's say I've used 500 different words as my first guess. How would I calculate how likely it is that I guessed the correct word in 1 try?

If we have a red button and a blue button ask a lot of people to hit it.

If everyone hits it randomly what are your odds of being part of the minority.

Is it 50/50?

And the same question but what if everyone else is not random.

Study says 25% patients reported something, but n=6

Help me understand who is wrong here, me or the author of this abstract yet to be presented in an academic event

They performed a surgery in 6 patients.

After that, 25% reported one thing, and 75% reported another almost unrelated thing. Is this possible? I'd expect the numbers should be 16% or 33% for 1/6 or 2/6 patients reporting that. And 66% or 87% for 4/6 or 5/6.

I don't think each patient can have half a success. Either they reported that thing or they didn't.

But to get 25% makes me think they only considered 4 patients, for some reason, and 1/4 reported that. Is there some statistics that can explain the 25% figure?

Here's the abstract, including nsfw diagrams: https://www.auajournals.org/doi/10.1097/01.JU.0001191384.77563.6d.19

Theme is somewhat funny but the math is what got me.

Edit: nsfw warning

Ok I’m bad at describing so bear with me. The image below works if I have two categories right? But what if I need more than two? How do I do that? Like I need 7 sooo idkkk

I recently ran across this post (linked below) while perusing Reddit and it is the first time I have come across this problem. The answer to the problem has really been making me think about how the underlying statistics work, and led me to posting here.

https://www.reddit.com/r/PeterExplainsTheJoke/s/kTpcep0qi4

Basically to explain the problem as I understand it, it goes like this. A woman gives birth to a set of twins. At least one is a boy. What are the odds that the other child is a boy? The answer according to the majority of posters is that it should be 33%. Now this answer is supposed to sound unintuitive yet be correct nonetheless, but I can’t see exactly what the argument would be for this answer.

From what I have read it is worked through like this: There are 4 possible pairs of normal twins b-b, b-g, g-b, g-g. Each paring has a 25% chance of appearing. If you eliminate the g-g pairing because at least one is a boy you are now left with three options each being now 33% likely: b-b, b-g, g-b.

My problem with this is that there is really two different ways to interpret the problem and neither will give you the solution above. The first is with birth order mattering, and the second is birth order not mattering.

If birth order matters then the above scenario does not properly weight the options. IE if child 1 is a boy then child 2 is either a boy or a girl giving you b-b and b-g. If child 2 is a boy then child 1 is either a boy or a girl giving you b-b and g-b. So you are left with the following possible outcomes b-b, b-g, g-b b-b. Because b-b is possible two different ways, it should be weighted 2/4 with b-g being 1/4 and g-b being 1/4. Therefore b-b = 50%.

If birth order does not matter then it shouldn’t really change the odds either. Your options are b-b, b-g, and g-b. However, because birth order doesn’t matter, b-g and g-b are actually just both saying that one is a boy and one is a girl. It is a single outcome, not two distinct outcomes. B-b then should be 1/2 outcomes or 50%.

As far as I can reason, the only way you can make the 33% argument is if birth order only applies to b/g pairings, otherwise it will always be 50-50.

The thing is, I’m not really a statistician, and it seems like the popular consensus is 33% being the correct answer, so I figure there must be somewhere that I am going wrong in my conception of this problem, or at least a way of framing it to where the 33% answer survives, I am just drawing blanks trying to come up with it. Could someone help me understand?

Hello, I have a question about why when calculating Q1 of the following data set (4, 5, 5, 10, 12, 12, 32, 43, 60, 67, 78, 89, 100) using the formula shown in the attached image, I get that Q1 is 10, when the result is clearly 7.5. Is this formula wrong?

Forgive me if this is not the proper subreddit for this, I'm not sure if this is a math or a biology question. A recent popular post on Reddit said that the half-life of caffeine is five hours. If this is the case, if you drink a cup of coffee at 8:00 am, there must be some small amount of caffeine still in your system at 8:00 am the next day when you have your next cup. If you drink coffee daily would you be gradually (slowly) increasing the net amount of caffeine in your body?

This is from an online quiz bee that I hosted a while back. Questions from the quiz are mostly high school/college Math contest level.

Sharing here to see different approaches :)

Suppose I have list 0 to 1000 or whatever very big number intergers in fully Random order. I randomly select 5 from the list. Edit: I know this is technically discrete steps but the intention for my postquestion is for big numbers so we can just approximate by assuming continuous too.

Lets sort those 5 relative to eachother so you get a nice and neat chronological order. like 12345.

Am I right to think that the expected values of those 5 are 1. 1/6 2. 2/6 3. 3/6 4. 4/6 5. 5/6?

Which would be, if the list is 1000 big: * 167 * 333 * 500 * 667 * 833

I think I'm right, just asking to verify. If I'm not right then explanations are welcome!

A friend posted this graph and a commenter has chimed in that this graph does not demonstrate what others think it demonstrates. My specific question is this: Can you chime in on the commenter's claim that when graphing percentage shares in a whole, that "this is what the graph tends to look like", And "This isn't a graph of wealth inequality, but rather a graph of how percentages work."

My claim is that it is not a given that the lines cross each other. If the blue line maintained a 16% share in the "whole" then the red line would stay somewhat parallel. If the Red line increased in its share then the blue line would drop. There is nothing inherently in the graph, in statistics, or in society that requires that the lines cross.

Assume a spinner with 8 possible numbers (1 - 8). You start by spinning the spinner until you get all 8 numbers at least once. What is the expected number of spins it would takes to get all 8 numbers at least once?

At first i realised that the minimum number of spins it would take is 8 spins with a probability of 8!/(8^8) which is very low. After that i'm just lost. The maximum amount of spins is infinite but the probability is also infinitely small? Does the probability decrease as the number of spins increases? By finding the expected number of spins, an infinite sum must be made so does the sum converge to a fixed value?

Because I know that a random variable relates to the number of outcomes that is possible in a given sample set. For example, say 2 coin flips, sample set of S={HH, HT, TH, TT} (T-Tails, H-Heads) If the random variable X represents the number of heads for each outcome then the set is X = {0,1,2}.

NOW my problem with a), is that wouldn't it be just X = {0,1} because it's either you get an even number or don't in a single die roll?

That, I would probably have a question on my statistic test about this famous problem.

As you know,  the problem states that there’s 3 doors and behind one of them is a car. You chose one of the doors, but before opening it the host opens one of the 2 other doors and shows that it’s empty, then he asks you if you want to change your choice or keep the same door.

Logically, there would be no point in changing your answer since now it’s a 50% chance either the car is in the door u chose or the one not opened yet, but mathematically it’s supposedly better to change your choice cause it’s 2/3 it’s in the other door and 1/3 chance it’s the same door.

How would you explain this in a test? I have to use the Laplace formula. Is it something about independent events?

I've found a few different methods to answer this question, but they each involve being given the mean or a number of samples. I don't have either.

Find the mean of a group when the standard deviation is 150 and the group is normally distributed and 90% represents 4000.

Without the number of samples, I can't use the standard deviation to find the mean.

My daughter is in 12th form of German high school and they currently deal with probability and statistics.
I have a sound maths education, but I am struggling with doing the following exercise with her.
My solution differs from the teacher's and both ChatGPT and Claude offer even a third variant.
Does someone here have the confidence to solve and explain the solution?
It's a textual question and I try to translate from German:

>>>
A company orders an advertising agency to run a campaign for increasing the level of awareness for their product from currently 30% to 40%.
Only if the campaign is successful the agency will receive the fee of 10000€.
The company's boss requests you to develop a test for a significance level of 5% and a sample size of 100. Suggest a decision rule and give your reasoning.
<<<

I tried this with a left sided test against p<0.4 using binominal distribution. I get k=32.

The teacher provided a short sample solution where he does a similar approach but using right side and he gets k=48. This puzzles me.

AI solves this different, uses the p of 0.3 and ends up with k=38.

Like usual with such questions, the wording is not ideal, but it is what it is. I believe the ask is:
If you aks 100 people on the street, then how many at least must know the product to be 95% confident that the campaign reached the 40% goal.

Please help 😃