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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what is wrong with this reasoning?

14% of people are left handed, if we want to find the chances of a brother and a sister both being left handed, we might be tempted to multiply .14 by .14. What is wrong with this reasoning when trying to find out the probability of both of them…
user8521
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Simple question about probability

I'm a bit confused about something. Let's say I want to cross a road to my friend's house. The probability of the road to be opened is $p$, and $1-p$ to be closed. So I know the probability for one direction at a time. What would it be if I would…
Ofek Pintok
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Modeling concurrent internet users

I'm feeling generous in the new year and want to open my Wifi connection to the public. I want to estimate the effect that $N$ additional users on my router would have on download times. In other words, how does my waiting time for an average piece…
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What's the expected value of working modules?

An electric system is made up of $k$ modules. In each module, there are $N$ resistors in series. What is the expected value of working modules if $m$ resistor break down? A module is not working if there is at least $1$ bad resistor in it. I can…
Botond
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Probability that at least $2$ of a group of $4$ people were born on the same day of the week

What is the probability that at least $2$ of a group of $4$ people were born on the same day of the week? My attempt: Probability that at least $2$ of a group of $4$ people were born on the same day of the week=1-probability that at most $1$ of a…
Rakesh Bhatt
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Probability a random permutation has no consecutive numbers next to each other

What is the probability that a random permutation of the integers $\{1,\dots,n\}$ has no two consecutive numbers next to each other? For example, for $n=4$ the permutation $2,4,1,3$ has no two consecutive numbers next to each other. However,…
user35671
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What is the probability that it takes more than seven rolls of a fair $6$-sided die to roll a six?

What is the probability that it takes more than seven rolls of a fair $6$-sided die to roll a six? The probability of rolling a six per roll is $1/6$. Therefore, the probability of rolling something other than a 6 is $5/6$. So wouldn't the…
Lucky12456
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Finding probability for general cases

For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1st exam is $p$. If he fails in one of the exams then the probability of passing in the next exam is $p/2$ otherwise it remains the same.…
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Finding probability of joint discrete rv

Let $X$ be poisson distribution with parameter $\lambda$ and $Y$ geometric with parameter $p$. Find $P(Y>X)$. ($\bf independent$) Attempt We know $p_X(x) = \frac{ e^{-\lambda} \lambda^x }{x!} $ and $p_Y(y) = (1-p)^{y-1} p$. Now, we have the…
James
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Consequences of being both independent and conditionally independent?

Suppose $A$, $B$, and $C$ are random variables. If $A$ and $B$ are independent, and they are also conditionally independent given $C$, can we conclude that either $A$ and $C$ are independent or $B$ and $C$ are independent? Or is there a case where…
Springo
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Probability the driver has no accident in the next 365 days

The time until the next car accident for a particular driver is exponentially distributed with a mean of 200 days. Calculate the probability that the driver has no accidents in the next 365 days, but then has at least one accident in the 365-day…
James
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(yet another) length of random segment

Take a random point $Z$, i.d. in [0,1], which defines a stick. Break the stick in two, (random i.d.). Take the left part of the broken stick and break it again in two (i.d.) You thus obtain three sticks. What is the expected length of the stick…
alexandreC
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Probability of a coin stack being greater than a value? What's wrong with my reasoning?

Basic probability question. Consider a pile of 9 coins where each could either be 1 cent or 10 cents and the distribution of the coin combinations is uniform. Knowing that the upper 4 coins are all 10 cents, what is the probability that the…
JobHunter69
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A disgruntled secretary problem - why my solution is incorrect

There are $n$ letters addressed to $n$ different people. The $n$ addresses are typed on $n$ envelopes. A disgruntled secretary shuffles the letters and puts them in the envelopes in random order, one letter per envelope. We are to find the…
Hendrra
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very simple conditional probability question

You know that a couple has two children. You go to the couple's house and one of their children, a young boy, opens the door. What is the probability that the couple's other child is a girl? If you list all possibilities for the sexes of two…
not bayes