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
4
votes
1 answer

How to compute the expected minimum Hamming distance with 3 strings

If we sample $3$ binary strings of length $n$, uniformly and independently, what is the expected minimum Hamming distance between the closest pair? Numerically, it seems to be asymptotic to $n/2$ but it would be great to know if there is an exact…
user35671
4
votes
4 answers

How calculate the number of possible different variations?

I feel stupid, but I don't know how to calculate how many possible variations I can get from for example three spaces (1|2|3) Normally I'd say: "well that is easy, just take the number of spaces (=3) and 3^3" But that doesn't work with two spaces,…
Blub
  • 165
4
votes
2 answers

Joint distribution of random variable with an order statistic

Let $X_1,...,X_n$ be i.i.d. with the distribution of the $X_i$ being nice and continuous. I'm interested in the expression of the CDF $F_{X_{(1)},X_j}(u,v)$. To be clear $X_{(1)} = min(X_i)$ and $X_j$ just one of the n i.i.d. random variables. I'm…
4
votes
1 answer

Bertrand's Paradox and uniform distribution

This is a problem from Hans-Otto Georgii's textbook. Recall the situation of Bertrand’s paradox, and let X be the distance of the random chord to the centre of the circle. Find the distribution density of X if (a) the midpoint of the chord is…
siegfried
  • 238
  • 1
  • 7
4
votes
2 answers

Probability to identify highest margin product.

Assume the following scenario. I can Sell P1 for a profit of 14% or sell it at a Loss of -7% Sell P2 for a profit of 11% Or sell it at a loss of -6% Sell P3 for a profit of 7% or sell for a loss of -1% Considering the…
user734995
4
votes
1 answer

Do lower weights affect choices. (This question is based off one when thinking about college applications with binding decisions)

Three events $A, B, C$. They are yes/no events. They are independent. $A$ is of greater weight/worth than $B$, and $B$ than $C$. In cases where multiple occur, only the greatest weight matters. You have the chance to increase the probability of $B$…
4
votes
1 answer

How my professor derived this CDF?

This was an example problem my professor went over in class. Let $X =$ uniform $(1,4)$ where $Y=(X-2)^2$ Find the CDF. He went on to derive: $F_Y(y)=P(Y\leq y) = P((x-2)^2 \leq y) = P(-\sqrt{y}\leq (x-2) \leq \sqrt(y))$ = $P(2 - \sqrt{y} \leq x…
Mark
  • 825
4
votes
1 answer

Minesweeper revisited

This is a followup query to the following: Minesweeper odds for this scenario, 2 different calculations I answered that query and now believe that my answer is wrong (explanation below). I ask professional mathematicians to respond. In my answer, I…
user2661923
  • 35,619
  • 3
  • 17
  • 39
4
votes
1 answer

Asymptotic moments of $\sqrt{n} \bar{X}$ when $X_i$'s are iid Cauchy distributed?

For a Cauchy distribution with density $f(x) = \frac{1}{\pi(1 + x^2)}$ , it doesn't have well-defined moments. Therefore both the law of large numbers and the central limit theorem can't apply to the distribution. For example, Given iid sample…
Tim
  • 47,382
4
votes
1 answer

probability of rolling a 6

Select a die from a bag containing 2 dice, one die has 6 on all faces, and the other is a fair sided die. Choosing one die at random, roll it, and get a 6. If you roll the same die, what is the probability that the next roll is also a 6? Would this…
4
votes
1 answer

Identically Distributed Uniform Variables U and 1-U

In this post: Exercise regarding Poisson processes and the uniform distribution It is noted that U and 1-U are identically distributed for the r.v. U which is uniformly distributed on (0,1). If a definition for two random variables being…
rhl
  • 305
4
votes
3 answers

Probability of losing packets

I am currently enrolled in an Intro to Networking course and I have been studying for an upcoming exam by doing practice problems in the course textbook. I came across this question that stumped me. It deals with probability, which I have always had…
Petefic
  • 141
4
votes
2 answers

Probability and marbles

My brother brings a certain number of his marbles to play with in my room. Each marble is distinct. He has 8 total marbles that are either red or blue. One day, I spotted two red marbles in my room. The probability that any two of his marbles (of…
4
votes
2 answers

Probability that at least one fails

A certain component of an electronic device has a probability of $0.1$ of failing. If there are $6$ such components in a circuit. What is the probability that at least one fails? The Answer is $0.47$. My Solution: At least $1$ means more than $1$…
Jon
  • 55
4
votes
1 answer

What can r.v.s mean?

I am reading "Introduction to Probability" 2nd edition (Blitzstein). He uses the abbreviation r.v for random variable which he explains. However, without introducing what "r.v.s" should mean, he uses it like this: So what do you think this means?…
That Guy
  • 1,309