Does it make sense to accumulate percentages this way? Do I really have a 17% chance of passing due to one of the improbable causes that are a fraction of 1%? This seems wrong intuitively. Source: https://knowyourchances.cancer.gov/your\_chances.html
This is a question I gave on a homework on a combinatorics lesson I'm teaching, but I just realized I'm unsure on the best answer. I'm pretty competent in general but this is the first time I've taught the course.
The sources I have been using suggest that 3!13!13!13!13! is the answer (3! ways to put 4 groups into a circular arrangement, then the 13! for the permutations of the cards in each suit) but I am second guessing myself.
If I instead wonder how many ways I can put the cards into a linear permutation with the same "suits all together" restriction, I am absolutely certain that there are 4!13!13!13!13! distinct arrangements. These strings would all be 52 cards long. Moving the first card to the last position gives a new linear permutation, but both of these lines can be bent into the same circle. I fact, I can repeat this process and still get another instance of this-line-makes-the-same-circle, so on and so on until I loop back to the line I started with. This means that counting the linear permutations overcounts the circular permutations by a factor of 52, and the best answer is actually 4!13!13!13!13!/52.
So which is it?
TLDR is the answer 3!13!13!13!13! , 4!13!13!13!13!/52, or something else entirely?
This is a question I gave on a homework on a combinatorics lesson I'm teaching, but I just realized I'm unsure on the best answer. I'm pretty competent in general but this is the first time I've taught the course.
The sources I have been using suggest that 3!13!13!13!13! is the answer (3! ways to put 4 groups into a circular arrangement, then the 13! for the permutations of the cards in each suit) but I am second guessing myself.
If I instead wonder how many ways I can put the cards into a linear permutation with the same "suits all together" restriction, I am absolutely certain that there are 4!13!13!13!13! distinct arrangements. These strings would all be 52 cards long. Moving the first card to the last position gives a new linear permutation, but both of these lines can be bent into the same circle. I fact, I can repeat this process and still get another instance of this-line-makes-the-same-circle, so on and so on until I loop back to the line I started with. This means that counting the linear permutations overcounts the circular permutations by a factor of 52, and the best answer is actually 4!13!13!13!13!/52.
So which is it?
TLDR is the answer 3!13!13!13!13! , 4!13!13!13!13!/52, or something else entirely?
Hi, I’m a software engineer with very little background in probability and statistics.
Recently, I’ve been playing Ludo on YouTube Playables, and I’ve started to wonder whether the dice rolls are actually fair.
In particular, when one of my pawns is a certain number of spaces ahead of an opponent’s pawn, (4 player game, 3 computer vs me) it feels like the opponent rolls the exact number needed to capture my pawn more often than I would expect from a fair six-sided die.
I realize this could simply be confirmation bias, so I’d like to test it properly rather than rely on intuition.
I can collect data from my games, but I’m not sure how to analyze it. How would I formulate and statistically test the hypothesis that the dice rolls are biased in situations where an opponent has an opportunity to capture my pawn?
Could someone explain what data I should collect, what statistical test would be appropriate, and the probability/math behind it in a way that’s accessible to someone without much statistics background?