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Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

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Lethal russian roulette (modifed)

$21$ players stand in the circle. Every player chooses aim for the shot - another player. No one can shoot themselves or into the air. What the probability that there are at least $2$ players that have taken aim at each other?
Xxx
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What is the standard deviation of dice rolling?

When trying to find how to simulate rolling a variable amount of dice with a variable but unique number of sides, I read that the mean is $\dfrac{sides+1}{2}$, and that the standard deviation is $\sqrt{\dfrac{quantity\times(sides^2-1)}{12}}$. I…
Olivier Grégoire
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Comparing Poisson variables

Let $X$ and $Y$ be two Poisson variables with different mean. Is there a better (as in more concise or numerically faster) way to compute $P(X\leq Y)$ than using $$ P(X\leq Y) = \sum_{y=0}^\infty P(Y=y) P(X\leq y) $$
Jens
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Refining the central limit theorem on discrete random vars

Let $x_i$ be iid nonnegative discrete random variables $E[x_i]=N/M$ for some integers $N, M$, variance $\sigma^2$ and higher moments known (finite). Then, the sum $\displaystyle S = \sum_{i=1}^M x_i$ will have $E[S]=N$. I'm interested in the…
leonbloy
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Translating mathematical problem statement into natural language

Let us consider following problem : One thousand tickets are sold at $\$1$ each for a color television valued at $\$350$. What is the expected value of the gain if you purchase one ticket? I would like to describe my basic problem related to this…
dato datuashvili
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Probability of winning an arbitrary game

I would like to know how to find the answer to this probability problem. Two players, $A$ and $B$, are playing an arbitrary game (no draw is possible). The winner is the player who wins two consecutive games. Player $A$ has $2/3$ chances of…
Provost
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Events A and B are independent such that $P(A)=6P(B)$

Events A and B are independent such that $P(A)=6P(B)$ and $P(A \cup B) =0.915.$ Find P(B). I know that $P(A \cup B)= P(A) + P(B) -P(A)P(B)$ Then $0.915=6P(B)+P(B)-6P(B)P(B) \\ \rightarrow 0.915=7P(B)-6P(B)^2$. $-6P(B)^2+7P(B)-0.915=0$ Letting…
Killercamin
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What is $P$ of either Heads or Tails having a lead $\geq 10$ at some point during game of $300$ flips?

Question refers to $P$ of getting lead of at least $10$ at any point during a game, with game lasting only $300$ flips. I tried to apply the formula given in an answer to a similar question here $P(X_n≥ (n+10/2))$ but that works out to summing…
Pseudoego
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Probability of winning a best of 3 out of 5 game

Two people play a series of independent games. Person 1's probability of winning any game is 0.6, which leaves 0.4 for Person 2. If they play a best of 5 tournament (3/5), find the following. (1)Probability that person 1 wins the tournament in 3…
Avalon-96
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Probability two students are paired

I'm wondering why my answer here is incorrect. The question is: John and Steve are members of a class of $20$ students. What is the probability that they are paired together? My thought was simply $1$ way to pair John and Steve and $20 \choose 2$…
ClownInTheMoon
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Example to illustrate difference between support and domain

Assume that X is a discrete random variable, I understand that the domain of X is the set of values it can take and the support of X is the set of values it takes with non-zero probability. Can someone give me an example of where 1) $S \subset…
Inquest
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Relation between Memorylessness and Independence

I was reading about Memorylessness and Independence and was wondering whether there is any relationship between the two. I realize that memorylessness is a property of a random variable of a particular distribution (such as X is a RV following…
Inquest
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The tea bag problem: probability of extracting a single bag of tea

Suppose you have a bunch of tea bags in a box, initially in pairs, like these: Let us suppose the box initially contains only joined pairs of tea bags, say $N_0$ of them (thus making for a total of $2N_0$ tea bags). Every time you want to make…
glS
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Finding probability of other child also being a boy

A man visits a couple who have two children.One of them, a boy, comes in to the room. Find the probability p that other is also a boy a) 1/3 b) 2/3 c) 1/2 d) 3/4 Correct Ans: a) 1/3 However I am getting answer as 1/2.My solution is as follows. The…
kabirkukreti
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Probability Question: Would A always have a greater chance of $A\cap B$?

My professor assigned a completely random question on our problem set. Basically, it goes: Sophie is 30 years old and majored in philosophy. As a student, she participated in anti-nuclear demonstrations and was deeply concerned with social justice.…
Anon
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