# Tagged Questions

This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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### Probability of Top Gear's alleged insulting number plate - requiring confirmation please [closed]

Please confirm or alter the calculations below which I believe to be correct based on 650 regional letter pairs for the 2nd and 3rd letters of the grouped three This UK number plate in question is ...
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### Probability of selecting the winning numbers in a lottery

I've been studying combinatorics for a while. I've solved a problem but I'm not sure if I'm right. I'll just copy-paste the problem here. In a lottery, six distinct numbers are selected at random ...
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### Likelihood Ratio and Neyman-Pearson factorization theorem

I'm looking at a family of distributions given by $P = \{P_{\theta} \quad | \quad \theta \in \{0,1\} \}$. I'm trying to prove that $$T(x) = \frac{p_{1}(x)}{p_{0}(x)}$$ (i. e. the likelihood ratio) ...
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### the coefficient of $t^{18}$ in $t^6(1+t+\cdots+t^5)^6$ equals the coefficient of $t^{12}$ in $(1+t+\cdots+t^5)^6$.

Let $X$ be the total from rolling 6 fair dice, and let $X_1,\ldots,X_6$ be the individual rolls. What is $P(X=18)$? Then the PGF of $X$ is E(t^X) = E(t^{X_1} \cdots t^{X_6}) = \frac{t^6}{6^6}(1+t+ ...
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### What is a mathematically rigorous justification for multiplying edge probabilities of a tree diagram

I was trying to understand why it was mathematically justified to multiply edge probabilities in a tree diagra and I came across the following question: Why do we multiply in tree diagrams? The ...