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 for Fighting Fantasy! What if I have the same skill but more life?

so I've been rereading my old fighting fantasy books and I thought of a problem I'm unsure of how to solve. In the book you fight various opponents by rolling two 6 sided dice and adding your skill (just a number), then you roll the dice for them…
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Chances of being picked last in a hat

A couple of friends and I are struggling with coming up with an answer to this question. It's seemingly simple but I need a little help. 6 people put their name into a hat. One by one, names are pulled without replacement. What are the odds…
KPD123
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Probability that out of 600 crabs 60 are still alive after 9 months.

A crabs' life expectancy can be modeled exponentially, and a crab lives 3 months on average. I am absolutely not sure about this, because there is nothing concerning this in our book, so I guess it was meant to be solved in some obvious/easy…
355durch113
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What is the probability that a pokemon gets frozen within 3 turns using ice beam?

Ice beam is a pokemon move that has a 10% chance to freeze the enemy pokemon each turn. What is the probability that I freeze the enemy pokemon if I have 3 turns? On one hand 'logically' the answer should be 30% On the other hand, if we add up all…
Jason
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Bridge probability problem

From volume 1 of Feller: North and South have 10 trumps between them ( trumps being cards of a specific suit) (a) find the probability that all three remaining trumps are in the same hand (that is, either East or West has no trumps) (b) if it is…
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Probability of Winning in Sports

In sports such as volleyball (prior to 1999), you can score a point only if it is your turn, with turns alternating until a point is scored. Suppose your probability of scoring a point when it is your turn is $p$, and your opponent's probability of…
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Expected number of blocks of identical weather

The problem is as follows: On a given day, the weather can either be sunny (with probability $0.4$), cloudy (with probability $0.4$), or rainy (with probability $0.2$). Assume weather is independent across days. Define blocks of weather to be the…
tkim
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What is the probability of getting $3$ triples before a single quad in a $52$ card deck?

Suppose I have a well shuffled standard deck of $52$ cards. I draw them one at a time (without replacement) and sort the chosen cards by rank so that it is easy for me to see pairs, triples, quads.... I want to know what is the probability of…
David
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Probability of multiple independent events occurring after repeated attempts

Suppose there is a bag of 10 identical octahedrons, one of which is a fair eight-sided die numbered 1-8. Randomly draw the one of the octahedrons out of the bag. If you draw the die, you must roll it. Put the octahedron back into the bag before…
ReiFox
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Chance of $7$ of a kind with $10$ dice

How can I calculate the probability of shaking $7$ of a kind using $10$ six-sided dice?
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Expected number of trials before I get one of each type

Say I have a population that I sample from without replacement. In this population there are $a_1$ members of type 1, $a_2$ members of type two and so forth up to $a_k$ of type $k$. What is the expected number of trials until I collect at least one…
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There are 6 white balls and 9 black balls. Probability of drawing two white, then two black?

From A First Course in Probability (9th Edition): 3.5 An urn contains 6 white and 9 black balls. If 4 balls are to be randomly selected without replacement, what is the probability that the first 2 selected are white and the last 2 black? This…
user251299
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Find the conditional probability of 6 appearing exactly once in $3$ rolls of a die given that it appeared at least once.

Did I find the correct probability? A fair die is rolled $3$ times. The conditional probability of 6 appearing exactly once, given that it appeared at least once. So,the combined probability that 6 appeared exactly once and it appeared at least once…
Onix
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Occurrence of 5 consecutive tails before occurrence of 2 consecutive heads

In repeated tossing of a fair coin find the probability that $5$ consecutive tails occur before occurrence of $2$ consecutive heads. My attempt: I tried to find the probability of non-occurrence of two consecutive heads in $n$ throws. Let $a_{n}$ be…
Maverick
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Bound on variance of function of a random variable

Suppose $0\leq X\leq 1.$ Suppose we are given that $\mathrm{Var}(X)\leq a$ where $a$ is some small constant. What are the best upper bounds we can provide on $\mathrm{Var}(f(X))$ if a) $f:[0,1]\mapsto\mathbb{R}$ is a Lipschitz function with…
Hedonist
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