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 .

105859 questions
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Probability of two people in a group of n people sharing the *exact* birthday?

I understand the solution to the birthday paradox. But I was wondering how I would calculate the probability of two people having the same age, or the exact birthday, down to matching years. I am thoroughly confused. Please help.
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Number of integers that do not show up

An integer is repeatedly drawn at random from $1, 2, . . . , 10$. What are the expected value and the standard deviation of the number of integers from $1, 2, . . . , 10$ that do not show up in $20$ drawings? Let $X_i$ be the random variable that…
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Players and tickets

You are among N players that will play a competition. A lottery is used to determine the placement of each player. You have an advantage. Two tickets with your name are put in a hat, while for each of the other players only one ticket with her/his…
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Probability of Getting a Red Ball

I have a simple and straightforward question. A box contains $n$ balls, of which $r$ are red ($r$ and $n$ are both positive integers, and $r \leq n$; suppose further that $n$ is even). Consider what happens when the balls are drawn from the box…
Noah A.
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In a queue for £1 tickets, there are $m$ people with a £1 coin and $n$ people with a £2 coin. What is the probability that everyone receives change?

I am selling raffle tickets for £1 per ticket. In the queue for tickets, there are $m$ people each with a single £1 coin and $n$ people each with a single £2 coin. Each person in the queue wants to buy a single raffle ticket and each arrangement of…
Bysshed
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Since when is 9/10 = 92%?

This is probably a more basic question than this site is used to, probably because I'm only 13, and as such I'd appreciate if you gave a more basic and simple explanation than the norm for this site. I was reading a BBC News article this morning and…
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The probability of repeating a test with a 30% chance of being wrong.

I got in a bit of an discussion with my dad about this and thought about it a lot. Would like some insight. So the question: if you have a test (ex: a virus antibody test) that returns positive or negative and has a 30% chance of having an incorrect…
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Colliding color balloons in a room

Suppose there are a total of $N$ balloons in a closed room out of which n are blue and the rest are red. After every unit of time,say a minute, any two balloons collide with independent probability $p$.The rule is when a red and a blue balloon …
AgnostMystic
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Conditional Probability or Intersection - Second Problem

The question that I asked at Is the Event a Conditional Probability or an Intersection? may be similar, but I'm confused over the following question from a different textbook. I'd be shocked if two textbooks make the same mistake! It's Example 2e on…
user53259
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Bias/Nonbiased Probability Puzzle Question

I got this puzzle that I need help on. I hope its not too easy because I really don't understand it. A bag contains 100 coins. 99 of them are fair and will give heads or tails with an equal probability. 1 biased coin will always yield heads. I…
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probability of at least one person having a gem of type $n$, etc.

(Probability Question) I have a number of $N$ types of gems that I have handed out to $M$ people, using some random probability function for each person. Thus: $$ \begin{align} P_1^1 + P_2^1 + P_3^1 + P_4^1 + \dotsb + P_n^1 &= 1 \\ P_1^2 +…
Bob
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Conditional Probability: John and Mary's registration cards

I am trying to solve a problem from a Dartmouth textbook (https://math.dartmouth.edu/~prob/prob/prob.pdf) Chapter 4.1 Ex 53. Disclaimer: I am not a student. I am just studying some probability questions from the text book. Here is the…
gdlamp
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Two players alternatively shoot a target, first person who hits two consecutive shots win.

Two players take turns shooting at a target, with each shot by player $i$ hitting the target with probability $p_i$, $i=1,2$. Shooting ends when two consecutive shots hit the target. What is the probability that the player who shoots first will…
Thief
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Inequality involving stochastic dominance in Likelihood Ratio Order

Problem: I am struggling for some time to show that a particular inequality holds or to find a counterexample to disprove it: Suppose you have two continuous random variables $X_1, X_2$ with densities $f_1$ and $f_2$, respectively, which are both…
P3rs3rk3r
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Probability concept that distinguishes likelihood of sequences 0110101011101... and 000000000000...?

Say we have a coin and want to decide if it is fair or not. We flip it many times. Consider two cases. Say the result is a sequence like 0110101011101... The result is 000000000000... In the first case the assumption that the coin is fair sounds…