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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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Probability two people will talk at the same time

The other day, I was talking to a friend, and then one of those lulls in the conversation came, where we had nothing more to say on the current subject and a new topic didn't immediately come to mind. We both decided to end the gap and start talking…
Ian Dalton
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The motivating properites of beta distribution and how its density function is developed?

The density of beta distribution is given by the following $$f(x\mid \alpha ,\beta ) = \frac 1 {\operatorname{B}(\alpha,\beta)} x^{\alpha - 1} (1 - x)^{\beta - 1}$$ where $$ \operatorname{B}(\alpha,\beta) = \int_0^1 x^{\alpha - 1} (1 -…
Ralph B.
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Probabilty of picking an irrational number

I've started to learn some probabilty and it made think about this question: let us assume we randomize virtually any number between 0 and 1. What is the probability for this number to be irrational?
catch22
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Asymptotic probability that two binomial variables are equal

$X_1,\ldots,X_k$ are independent random variables distributed like $\text{Binomial}[n,p]$. What is the probability that they are all equal, as a function of $k$ $p$ and $n$, when $n$ is very large? Currently I have two solutions. Solution A is…
Erel Segal-Halevi
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How many strings of 8 English letters are there...?

1) That contain at least one vowel, if letters can be repeated? $26^8-21^8$ 2) That contain exactly one vowel, if letters can be repeated? $8\cdot 5\cdot 21^7$ 3) That start with an X and contain at least one vowel, if letters can be…
user1038665
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If n people enter a hall through any one of n doors, what is the probability at least one door is not used?

The probem is I have 2 conflicting solutions. Solution 1: Since there is $n$ people who each choose any one of $n$ doors, the total number of ways $n$ people enter the hall is $n^n$. (correct?) then I used, $P($one door not chosen$)=1-P($all doors…
Keegs
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Probability of choosing same color ball 2 times in a row

My son's teacher and I are having a debate about the correct answer to a question. I have an engineer at hand and he has a mathematician so we both feel well supported. We've also both researched the internet and found answers that we feel support…
K. Hartwig
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Alice and Bob are flipping coins...

Alice and Bob are playing a game. They randomly determine who starts, then they take turns flipping a number of coins (N) and adding them to a growing pile. The first one to collect their target number of tails (T) wins. When Alice's variables are…
Teller
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Counting outcomes for coin tosses

Don't laugh, this is a dumb question, but my brain just doesn't work mathematically. A question in my math class says A coin is tossed 4 times. Compute the probability of at least 2 tails occurring. OK, so I know I figure out how many total…
SuzieQ
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How do I solve this probability problem of randomly drawing balls from a urn?

In an urn there are $a$ azure balls and $c$ carmine balls, $ac\ne0$. To begin with, you randomly pick a ball, throw it away, and then each time you randomly pick a ball, if it has the same color with its predecessor, throw it away, otherwise put it…
xzhu
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Probability of "clock patience" going out

Here is a question I've often wondered about, but have never figured out a satisfactory answer for. Here are the rules for the solitaire game "clock patience." Deal out 12 piles of 4 cards each with an extra 4 card draw pile. (From a standard 52…
Cheerful Parsnip
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Probability that the first cell is empty

There are three distinctive balls to distribute to 8 cells. Each cell can hold multiple balls. I'm trying to figure out the probability $P(A)$ that, after distribution, the first cell is empty. My thoughts: In total, there are $8^3$ possibilities to…
wkwilliam
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What's the probability that the other side of the coin is gold?

4 coins are in a bucket: 1 is gold on both sides, 1 is silver on both sides, and 2 are gold on one side and silver on the other side. I randomly grab a coin from the bucket and see that the side facing me is gold. What is the probability that the…
David Faux
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Is order of variables important in probability chain rule

Is the order of random variables important in the chain rule? I mean, is this true: $P(A,B,C) = P(A)\times P(B|A)\times P(C|A,B) = P(C)\times P(B|C)\times P(A|B,C) = P(C,B,A)$? If it is, what is the meaning of such order? Thank you.
Martin08
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Kelly criterion for multiple gambles

Kelly says you should invest $x\%$ of your bankroll in a gamble: $$x = \frac{pE-1}{p-1}$$ where $p$ is the probability of winning and $E$ is the expected payoff multiplier if you win (i.e. $E$ times how much you bet). But lets say you have two…
Wuschelbeutel Kartoffelhuhn
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