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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Probability of tossing a fair coin with at least $k$ consecutive heads

Tossing a fair coin for $N$ times and we get a result series as $HTHTHHTT\dots~$, Here '$H$' denotes 'head' and '$T$' denotes 'tail' for a specific tossing each time. What is the probability that the length of the longest streak of consecutive…
Benson
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What's the probability of getting 1000 heads in a row?

I'm reading The Master Algorithm by Pedro Domingos and I'm having a hard time understanding something he wrote on page 74: "If you do a million runs of a thousand coin flips, it's practically certain that at least one run will come up all heads." My…
user452038
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Probability of getting a $7$ in Minesweeper

Let's say you have a $30$ by $16$ grid and $99$ mines. What is the probability of having at least one empty block surrounded by exactly $7$ mines? For the sake of this question, assume that the mines are generated randomly.
Paul
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Shooting bullets

This is from http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/May2014.html Every second, a gun shoots a bullet in the same direction at a random constant speed between 0 and 1. The speeds of the bullets are independent uniform random…
curious
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Probability of iid random variables to be equal?

Suppose $X_1$ and $X_2$ are iid random variables. I want to determine $P(X_1=X_2)$. If they are integer-valued random variables, then $$P(X_1=X_2) = \sum_{i \in \mathbb{Z}} P_{X_1,X_2}(i,i) = \sum_{i \in \mathbb{Z}} P_{X_1}(i)^2. $$ If they are…
Tim
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Probability of of an event happening at least once in a sequence of independent events?

I want to find the probability of flipping heads at least once if you flip a coin two times. The possible outcomes (we don't care about the order) are (each equally likely) $TT$, $TH$, $HT$, $HH$. Three out of four have an $H$ in them, so the…
Ovi
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Funny(?) Probability Problem

So I ran accross the following problem today on a forum: "In an attempt to reduce male birth rates, feminists have passed a law which forces families to stop having children after their first male child. After this law is passed, what is the…
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What makes random variables exchangeable and what is implied by exchangeability?

Consider a $d$-dimensional random vector$\ X=(X_j)$. $\ X$ is called exchangeable if $\ (X_1,\ldots,X_d)\mathrel{\overset d =} ({X_{{j_1}}},\ldots,X_{j_d})$ for any permutation$\ j_1,\ldots, j_d$. If$\ X_j$ are iid,$\ X$ is exchangeable. The…
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Probability that a character kills the boss in a 3 versus 1 fight

In a RPG game, your three characters A, B and C fight a boss. The boss has $1000$ hp. The attacks are sequential: A attacks then B attacks then C attacks then A attacks again, etc. Character A can do any integral amount of damage between $25$ and…
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Is there a significance to the asymptotic probability of at least one occurrence of an event in n attempts?

Let's look at the set of the probabilities of having at least one occurrence of an event if we make $n$ attempts, where the probability of the event occurring is $1/n$. For example, if we are looking at the probability of the occurrence of rolling a…
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Coin Tossing Game Optimal Strategy

I was recently asked this question in an interview, but was completely stumped as to how to even begin answering it - it's been bugging me ever since, and I thought it was quite a nice question, so hopefully someone on here can help me out. Any help…
Boris
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Probability that Ken and John set next to each other

A group of ten people sits down, uniformly at random, around a table. Ken and John are part of this group. Determine the probability that Ken and John sit next to each other. There are $10!$ ways to arrange the seating for everyone, there are…
lzc
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Calculating the probability that at least one of a series of events will happen

I want to calculate the probability of at least one event happening in a series of multiple events. For example, let's say the probability of each event happening are: Event 1: 2/21 Event 2: 1/10 Event 3: 7/15 Event 4: 9/16 Event 5: 3/10 What is…
JSW189
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Glass Bridge Game in Squid Game (Episode 7/ Game 5)

Spoilers for Squid Game. In the show, there is a game where people try to cross a bridge, made of $n=18$ rows of 2 side by side glass panes, which they must cross one row at a time. One glass pane can support a person while the other will break,…
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Is probability determined by perspective?

My question: is probability determined by perspective? The scenario that raised the question for me: Initial condition: The Monty Hall problem. We know the contestant’s original choice of door #1 (of 3 total) is only correct 33% of the time. …
Burke
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