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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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Ordering of a deck of cards

If you shuffle n cards as follows: Go through the deck one card at a time and at each card, flip a fair coin. If the coin comes up head, then leave the card where it is, and if it comes up tails move that card to the end of the deck. For example,…
lord12
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Expectation of supremum

Let $x(t)$ a real valued stochastic process and $T>0$ a constant. Is it true that: $$\mathbb{E}\left[\sup_{t\in [0,T]} |x(t)|\right] \leq T \sup_{t\in [0,T]} \mathbb{E}\left[|x(t)|\right] \text{ ?}$$ Thanks for your help.
mellow
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Very probable event occuring at least once during $n$ trials

Assume that Bob carries eggs from point $A$ to $B$. He can carry $1$ egg each time. Let the probability that Bob breaks an egg be $0.99999$ which is almost a certain event (for me). If Bob carries $100$ eggs separately, can we say the probability of…
Ricardo Cristian Ramirez
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A question on CLT from Durrett.

I have a question from Durrett which I don't quite get the solution. The question is and the solution is I think I understand up to when $|S_n - n| \leq n^{2/3}$ is an event w.p.1, this is because $P(|S_n - n| \leq n^{2/3}) = P(|S_n - n|/\sigma…
jderzol
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The probability theory around a candy bag

Consider a candy bag that contains $N=100$ candies. There are only two types of candy in the bag. Say the caramel candy and the chocolate candy. Nothing more is known about the contents of the bag. Now, you are going to draw (randomly) one candy at…
Martin Gales
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How to buy a car optimally in this case?

X has a car. Its value is unknown yet, but between 0 and 1000, uniformly distributed You offer a price to buy the car. If price < value, you can’t buy. If price >= value, you can buy, give the price of money to X. (for example, if value is 200,…
Jack
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If $A$ and $B$ are independent, what can we say about $P(X\mid A,B)$?

Given two independent events A and B, what can we say about $P(X\mid A,B)$ ? Is the following correct ? $$P(X\mid A,B) = \frac{P(A,B\mid X)P(X)}{P(A,B)}\tag{Bayes}$$ $$P(X\mid A,B) = \frac{P(A\mid X)P(B\mid X)P(X)}{P(A)P(B)}…
GuillaumeThomas
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If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form $7^{m}+7^{n}$ is divisible by 5 is

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form $7^{m}+7^{n}$ is divisible by 5 is $A. 1/4$ $B. 1/7$ $C. 1/8$ $D. 1/49$ I did this: Let $m>n$ (Clearly m and n can't be equal because…
Apurv
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Probability of Poisson event occuring at least 3 times in given interval

At a parking garage, automobiles enter at a rate of $1$ car every $2$ minutes. I need to find the probability that the number of automobiles entering the garage during any $2$ minute period exceeds $3$. I know $\Pr(x \gt 3)= 1-\Pr(x\le 3)$. So,…
pgrado
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Random Variable Vs. Probability Function Intuition?

In a book on probability I'm reading they begin by defining random experiment, outcome, sample space & event, then using these notions they define & a probability space in terms of the sample space, a sigma field & a probability function. After…
Prob
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Independent Events- Indicator Functions

I can't seem to prove that two events are independent iff their indicator functions are independent discrete random variables. I was hoping to see a proof of this as I cant seem to find a proof in any of my notes nor online. Thanks
Raul
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Stationary Distribution of Doubly Stochastic Markov Chain

For a doubly stochastic markov process defined by a n by n transition matrix, does the stationary distribution go to p = 1/n for each state? If so, why?
Dan Schwartz
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Throw a die $N$ times, observe results are a monotonic sequence. What is probability that all 6 numbers occur in the sequence?

I throw a die $N$ times and the results are observed to be a monotonic sequence. What is probability that all 6 numbers occur in the sequence? I'm having trouble with this. There are two cases: when the first number is 1, and when the first number…
TRY
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How do I calculate the probability of getting 10 unique members of a set given random selection with replacement?

Assume I have a set of 20 numbers. Each number in the set is unique. I am able to retrieve one number at a time from the set with the probability of retrieving any one member of the set being equal. How would I go about determining the probability…
tabdulla
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Rumors told between $n+1$ people

In a town of $(n + 1)$ inhabitants, a person tells a rumor to a second person, who in turn repeats it to a third person, etc. At each step the recipient of the rumor is chosen at random from the $n$ people available. (a) Find the probability that…
TheNotMe
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