Tagged Questions

278 views

What is the probability that A will win…

Two players are rolling two dices, if they get 6 Player A wins, if they get 7, player B wins, else they rolling the two dices again... What is the probability that A will win? I'd like to get any ...
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Expected value over many trials

I am a poker player and was talking to my friend about expected value. He claimed that if you play far enough above your bankroll, expected value can be negative, even if you have a skill edge. I ...
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Finding a specific sequence of digits in pi

Looking at the pifs project on GitHub and this question on SO has made me curious as to how feasible it is to find a specific sequence of digits within Pi. Essentially, on average, how many digits of ...
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Find the sum of a probability of dice roll that is prime.

Consider rolling n fair dice. Let p(n) be the probability that the product of the faces is prime when you roll n dice. For example, when n = 1, one die is rolled and the probability that the result is ...
976 views

Does a randomly chosen series diverge?

Pick a point at random in the interval $[0,1]$, call it $P_1$. Pick another point at random in the interval $[0,P_1]$, call it $P_2$. Pick another point at random in the interval $[0,P2]$, call it ...
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why generating function $A(z) = 1 + z + z^2 + \cdots$ can be denoted as $\frac{1}{1-z}$

It is easy to see that $1 + z + z^2 + \cdots$ is equal to $\frac{1}{1-z}$ when $1 > z > 0$ and for $z >= 1$, they are not equivalent. So I have thought $\frac{1}{1-z}$ is just a short for the ...
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Discrete Math Subsets of a Set

A pizza parlor has six meat toppings and four vegetable toppings that can be added to a pizza. Pizzas also come in three different sizes. How many pizzas can be ordered that have at least one meat ...
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How to find sequence from set of values

I have set of probability values arranged in ascending order, p1<p2<p3<...<pM. Now I want to assign set of numbers in the same manner in which probabilities are increasing. It means I ...
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Convergence condition of infinite cosine product

Please show that, given that $\sum_{k\ge1}c_k^2=\infty$ and $c_k\rightarrow 0$, $$\lim_{n\rightarrow\infty}\prod_{k=1}^n\cos{tc_k}=0$$ for every $t\neq0$. (All variables here are real numbers.) The ...