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
9
votes
4 answers

Probability of at least N events occuring

I have a series of N events, each with its own probability of occurring. How would I calculate the probability that at least M of the N events actually do occur? I think this is conditional, in that getting at least M occurrences depends on getting…
Corv
  • 103
9
votes
2 answers

How rare is it to get a $8$ in minesweeper? (Bruh reputation requirments)

I need help on this, ignore if its already answered. Ok so today i was wondering, could you get a $8$ in minesweeper and how rare it is? All i know is that it will be rare. Very rare indeed. I dont really know how to say it. Its so annoying to be…
9
votes
2 answers

Probability that new baby born is a boy in a nursery

There are $2$ boys and unknown number of girls in a nursery. A new baby is just born inside the room. We pick randomly a baby from the room, it turns out that the baby is a boy. What is the probability that the new baby just born is a boy? We can…
9
votes
4 answers

Examples of the events for which we cannot assign "meaningful" probabilities

Quote from the book I'm reading: Any collection of possible outcomes, including the sample space $\Omega$ and its complement, the empty set $\emptyset$, may qualify as an event. Strictly speaking, however, some sets have to be excluded. In…
9
votes
2 answers

Calculating probabilities over different time intervals

If there was a 10% chance of an event occurring over a year, how would I work out how likely this event is to happen per month, per day etc? Now because if, using per month as an example, if it occurs in January it cannot happen again for that…
sxthomson
  • 193
9
votes
2 answers

Probability to starve

First of all, I'm sorry if I'll use some game related terms, but that's where the question that bugged me for the last week came from. Let's say, we have a mana pool of size $M$, and we can cast a spell that costs $n$, with $n < M$. The spell has a …
kaharas
  • 1,034
9
votes
7 answers

Conditional probability - sum of dice is even given that at least one is a five

Question: Calculate the conditional probability that the sum of two dice tosses is even given that at least one of the tosses gives a five. I'm a bit confused by this. Shouldn't the probability just be 1/2, since we know that at least one of the…
Gummy bears
  • 3,408
9
votes
2 answers

Cans on a shelf

6 cans are placed on a shelf in a circular arrangement. After tidying and cleaning the kitchen, the cans are placed again in new, random positions around a circle. What is the probability that none of the cans are in their initial positions or…
Pradeep Suny
  • 1,603
9
votes
2 answers

Binomial random variable with number of trials being a Poisson random variable

Let $Y$ be the number of heads in a an $X$ toss sequence of flipping a coin with probability $p$ of heads. Show that $Y \sim \mathrm{Pois}(p \lambda)$ if $X \sim \mathrm{Pois}(\lambda)$.
darksky
  • 507
9
votes
3 answers

Does repeated activity increase the probability of a specific event happening?

I am hoping that this is not too basic a question for this site, but I am seeking to better understand a conversation I have had with my more mathematically inclined friend. The discussion was around the probability of an event occuring with…
Chris
  • 193
9
votes
1 answer

How does the answer to Feynman's Restaurant Problem change if $M$ is not restricted to a single value?

First, the background: Feynman's restaurant problem asks how we can maximise the total rating of the meals we eat at a restaurant with $N$ items on the menu, given that we know up-front that we are going to eat $M$ meals there. I have transcribed…
AakashM
  • 574
9
votes
3 answers

Cat / mouse probability question

There exist 7 doors numbered in order from 1 to 7 (going from left to right). A mouse is initially placed at center door 4. The mouse can only move 1 door at a time to either adjacent door and does so, but is twice as likely to move to a lower…
David
  • 1,702
9
votes
4 answers

Is it "bad form" to count the number of outcomes in an event to compute a probability?

I've been reading this very interesting blog post entitled "A review of probability theory" from Terence Tao. Here are a few quotes from the blog post: Elements of the sample space $\Omega$ will be denoted $\omega$. However, for reasons that will…
9
votes
4 answers

Probability of drawing exactly $1$ ace upon drawing $2$ cards from a deck

I got this question and answered it incorrectly. I haven't yet seen the correct answer. The possible answers were: $\frac{4}{52}$ $\frac{16}{221}$ (my answer) $\frac{2}{52}$ $\frac{32}{221}$ My reasoning is the following: Event A: Card is not…
E. Sundin
  • 193
9
votes
1 answer

Advanced airplane problem

I recently came across a quite interesting problem: "One hundred passengers are lined up to board a full flight. The first passenger lost his boarding pass and decides to choose a seat randomly. Each subsequent passenger (responsible enough to not…