What is Probability: Definition and 1000 Discussions

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.

View More On Wikipedia.org
Recent contents Top users
  1. P

    Probability of drawing a kind from a deck of poker

    Homework Statement Find the probability that a hand of five cards in poker contains four cards of one kind. Homework EquationsThe Attempt at a Solution Solution given in the book:[/B] By the product rule, the number of hands of five cards with four cards of one kind is the product of the...
  2. U

    MHB Should You Play? Analyzing a Game with Probability & Strategies to Fix it

    Part 1: Your friend wants to play a game. You will roll two dice. If the sum of the dice is 8 or higher you win \$2, from 5-7 you win \$1, and from 2-4 you lose. You pay \$10 to play the game. Should you play? Explain. (Hint: Construct a probability distribution and find the mean) Part 2: Fix...
  3. H

    MHB Probability of winning a point on serve in tennis

    Hello, my question about calculating the probability in tennis I know that to calculate Pwos (probability of point won on oun serve ) for each player the following formula is used... # P(no Fault) -The probability a player's first serve not faulting # P(win/no Fault) -The probability a player...
  4. MIIF

    MHB Probability of Spin Resulting in Even # or <4

    I tried to answer it and got 3/4 or 6/8 after using the union set operation for 4/8 or 1/2 and 3/8, based on what is being asked in the problem...
  5. Physiona

    Office Ratio & Probability Question

    QUESTION: Office is a small office. In the morning of day 1 the ratio of male to female workers in the office is 15 : 7. In the evening of day 1 the unsimplified fraction of male to female workers in the office is 164 males entered the office at lunchtime and stayed for the...
  6. N

    MHB What is the probability of selecting two males given that both are grey?

    So I am having more problems with my homework... For this problem, assume there are 6 grey females, 2 grey males, 6 white females, and 2 white males. Two mice are randomly selected. What is the probability of selecting two males given that both are grey? So for selecting two males, I was...
  7. N

    MHB Conditional Probability and Venn Diagrams

    I am having a hard time with the following exercise: Assume for this problem that the company has 8 Chevrolets and 4 Jeeps, and two cars are selected randomly and given to sales representatives. What is the probability of both cars being Chevrolets, given that both are of the same make? I...
  8. resurgance2001

    Probability No Member Gets >1 Medal: Math Club

    Homework Statement There are 15 members of a maths club. There are 4 different medals to be randomly given to the members of the club. What is the probability that no member will receive more than one of the medals. Homework Equations Try to find the number of combinations where no member...
  9. N

    MHB Help with Math Homework: Conditional Probability - 19/30

    Hey! I need help with my Math homework :( The question is the following... There are 5 history courses of interest to Howard, including 3 in the afternoon, and there are 6 psychology courses, including 4 in the afternoon. Howard picks a course by selecting a dept at random, then selecting a...
  10. F

    Probability of getting an odd number-conditional probability

    Homework Statement Homework Equations - The Attempt at a Solution Probability of getting an odd number if the chosen dice was biased = P(O|B) from the tree diagram , P(O|B) = 1/4 Could someone check my answer please ?
  11. D

    Conditional probability reasoning problem

    Homework Statement Out of all the products a company makes 2% is damaged. During the routine control of the products, the products are put to a test which discovers the damaged ones in 99% of the cases. In 1% however it approves the damaged item as a working one and vice versa. Find the...
  12. L

    Basic probability, conditional probability

    Homework Statement what is the probability that a component which is still working after 800 hrs, will last for at least 900hrs Homework Equations conditional probability P(E|A) = ( P( E ∩ A) ) / ( P(A) ) The Attempt at a SolutionIm just checking my own understanding if this problem is...
  13. Muthumanimaran

    Finding the probability of transition

    Homework Statement The question is attached below Homework Equations $$P_{i \to n}(t)=\frac{|4H_{ni}|^2}{|E_{n}-E_{i}|^2}\sin^2\bigg[ \frac{(E_n-E_i)t}{2\hbar} \bigg]$$The Attempt at a Solution for simplicity I kept k=1 I don't know whether my approach is correct. That is I am not sure...
  14. E

    I Probability density of an exponential probability function

    I have a model where the probability is spherically symmetric and follows an exponential law. Now I need the probability density function of this model. The problem is the singularity at the origin. How can I handle this? P(r) = ∫p(r) dr = exp(-μr) p(r) = dP(r)/(4πr²dr) One way I tried to...
  15. P

    Probability of getting 3 out of 4 numbers correct

    Problem statement: In a lottery, players win a large prize when they pick four digits that match, in the correct order,four digits selected by a random mechanical process. A smaller prize is won if only three digits are matched. What is the probability that a player wins the small prize...
  16. Monoxdifly

    MHB Probability of Keeper Fending Off Penalty Kicks 3/5 Times

    A professional goalkeeper can fend off a penalty kick with the probability of \frac{3}{5}. In an event a kick is done 5 times. The probability of that goalkeeper being able to fend off those penalty kicks 3 times is ... A. \frac{180}{625} B. \frac{612}{625} C. \frac{216}{625} D. \frac{228}{625}...
  17. J

    Probability that more girls than boys go on the field trip

    Homework Statement Homework Equations First use equations to find out number of boys n number of girls. Then use probability concepts. The Attempt at a Solution Number of boys + number of girls = 12 Boys = Girls + 2 So we get Boys = 7, girls = 5. Select more girls than boys in a group of 3...
  18. benorin

    B Probability and Death Sentences

    Originally posted by Galileo in the thread I started called Bad Math Jokes on top of pg. 4: _____________________________________________________________________________________________________________________ Not so much a joke as a brainteaser. Three prisoners, strangers to each other, were...
  19. K

    Am I justified in using the binomial distribution?

    Homework Statement 12 non-distinguishable attacks from President Snow land in Panem’s 12 districts in a particular week. Assume the attacks are located randomly, with each configuration of attacks equally likely. What is the probability that some district had more than 1 attack? Homework...
  20. M

    MHB How Should I Start My Probability Question to Get the Best Help?

  21. Zeynel

    B Probability of loto hitting a specific place

    Someone asked me this question. The numbers are real. İn Turkey there are 957 cities where Loto is drawn every week. In the last 5 years the big prize was drawn at one location 26 times. What is the probability that a single location will get the big prize 26 times in 5 years. I think, though...
  22. benorin

    B The Drunkard's Walk: A Discussion of the Text

    This thread is for us to discuss the text The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow, and by that I mean for me to ask questions of you, those of you who will suffer me, my experts in probability, the PhysicsForums readers, on things I'm interested in from the text...
  23. B

    B Calculate probability of getting 2 red balls

    Hi, I'm struggling with a basic probability question and I need some insight into this problem. I can solve the problem, but its a really inefficient and time consuming way. The problem: There are 10 blue balls and 2 red balls in a jar. Calculate the probability of drawing 2 red balls if 4...
  24. M

    MHB Probability that someone has the disease

    Hey! :o The percentage of people that have a disease A is $0,01$. We apply twice a test for that disease, each of which give the correct answer with probability $0,95$. What is the probability that someone has that disease if at least one test is positive and what is the probability if both...
  25. chwala

    Statistics: probability distribution problem

    Homework Statement two indepedent observations ##X_1## and ##X_2## are made up of the continuous random variable having the probability density function ## f(x)= 1/k##, and ## 0≤x≤k## find a. the cumulative distribution of ##X## b. Find the probability distribution of M, the...
  26. E

    MHB What is the probability that one is hired and one is not?

    I cannot get past this question: Assume that 12 people, including the husband and wife pair, apply for 5 sales positions. People are hired at random. What is the probability that one is hired and one is not? The sample space is C(12, 5). I tried finding first the probability that one is hired...
  27. M

    MHB Probability: twice the same number

    Hey! :o We consider the following game: We can roll a dice until a number appears twice. We can then write down as many points as the times that we rolled the dice. Let $X$ be the random variable that describes the points that we get at each game. I want to calculate the probabilities...
  28. K

    Probability Problem -- pulling colored balls from a box randomly

    Homework Statement Bob had a box containing 9 green balls and 1 white ball. A Bob's friend removed one ball from the box without telling Bob what was its color. Now what's the probability for Bob picking up one green ball from the box? Homework Equations [/B] Not aware of "formulas", I just...
  29. R

    Bayesian Probability Distributions

    Hi, I was having some trouble doing some bayesian probability problems and was wondering if I could get any help. I think I was able to get the first two but am confused on the last. If someone could please check my work to make sure I am correct and help me on the last question that would be...
  30. E

    MHB What is the Probability of Selecting at Least One Odd Numbered Ball?

    The final question in my homework says: Assume the balls in the box are numbered 1 through 8, and that an experiment consists of randomly selecting 3 balls one after another without replacement. What probability should be assigned to the event that at least one ball has an odd number? I have...
  31. Danny Boy

    A Probability of obtaining general quantum measurement outcome

    The Fundamental Theorem of Quantum Measurement is stated as follows: Every set of operators ##\{ A_n \}## ##n =1,...,N## that satisfies ##\sum_n A_n^{\dagger}A_n = I## describes a possible measurement on a quantum system, where the measurement has ##n## possible outcomes labeled by ##n##. If...
  32. F

    MHB Probability of same results for 2 pools

    The question is “What is the probability of one person buying a single ticket for two different football pools and ending up with the same numbers”? The football pool used is a 10 by 10 array with the numbers 0 through 9 randomly assigned along the x and y axis. One axis is team A, the other...
  33. lfdahl

    MHB What is the Probability of Distances in an Equilateral Triangle?

    A point $P$ is chosen at random with respect to the uniform distribution in an equilateral triangle $T$. What is the probability that there is a point $Q$ in $T$ whose distance from $P$ is larger than the altitude of $T$?
  34. W

    I Effect of momentum distribution on probability density

    Hi all, I have the following query: I understand that the "make-up" of momentum probability density ##|\tilde{\Psi}|^2## has an effect on the motion of the spatial probability density ##|\Psi|^2##. For example, a Gaussian ##|\tilde{\Psi}|^2## centred far to the right will cause ##|\Psi|^2## to...
  35. Mayan Fung

    I A seemingly simple problem about probability

    My friend is now taking an introductory course about statistics. The professor raised the following question: A light bulb has a lifespan with a uniform distribution from 0 to 2/3 years (i.e. with a mean of 1/3 years). You change a light bulb when it burns. How many light bulbs are expected to...
  36. AirRecce

    General formula for a combination of four categories

    Homework Statement Say I have four categories which make up a "whole" that I'll call a unique "deal". Each deal can have "I" properties, "J" investors, "K" mortgages, and "L" credit lines, where "I" and "J" must be integers greater than zero and "K" and "L" are non-negative integers (i.e. 0 or...
  37. LarryS

    I Probabilities for degenerate eigenvalues?

    In non-relativistic QM, given a wave function that has a degenerate eigenvalue for some observable, say energy. There is a whole subspace of eigenvectors associated with that single degenerate eigenvalue. How is the measurement probability for that degenerate eigenvalue computed from the...
  38. M

    MHB Conditional Probability with 3 Events

    I'm currently stuck on a question that involves conditional probability with 3 events. This is a concept that I'm having the most trouble grasping and trying to solve in this subject. I am not sure how to start this problem. The Question: Given that P(A n B) = 0.4, P(A n C) = 0.2, P(B|A)=0.6...
  39. M

    MHB Probability : Voting problem - Game strategy

    Hey! :o I am looking the following: There are 1 Million voters. 2000 of them know exactly that they will vote for A, but the other 998000 will decide if whether they will vote for A or B in the voting booth using a coin. With which possibility will A get more votes? At a quiz we get...
  40. alijan kk

    Probability of Getting Head or 4: 7/12

    Homework Statement If a coin flipped and one die is thrown, what is the probability of getting a head or a 4 ? Homework EquationsThe Attempt at a Solution Sample Space={ H,1 H,2 H,3 H,4 H,5 H,6 T,1 T,2 T,3 T,4 T,5 T,6 } Event={ H,1 H,2 H,3 H,5 H,6 T,4 } probability is 6/12 if i don't do it...
  41. V

    MHB Corresponding character matching probability

    I have a dataset of protein, consisting of 10000 sequence each, having length Si , where 1<=i<=10000. Now, I extracted k-mer "a" from the 1st sequence. The probability of occurrence of amino acid (character of protein sequence) is given by its frequency in the dataset. If I choose k-mer "b" from...
  42. Y

    MHB Calculating Geometric Probability on a Round Table

    Hello all, I have a question related to geometric probability. I think I solved it, but not sure, would appreciate your opinion. We are given a round table with a radius of 50cm. At the center of this table there is another circle, with a radius of 10cm. A coin with a radius of 1cm is thrown...
  43. T

    Stochastic calculus:Laplace transformation of a Wiener process

    Homework Statement I am asked to show that E[\exp(a*W_t)]=\exp(\frac{a^2t}{2}) Let's define: Z_t = \exp(a*W_t) W_t is a wiener process Homework Equations W_t \sim N(0,\sqrt{t}) The Attempt at a Solution I want to use the following formula. if Y has density f_Y and there's a ral function g...
  44. Avatrin

    I Equality in conditional probability

    Hi In Dudas Pattern Classification, he Writes that P(x,\theta|D) can always be written as P(x|\theta,D)P(\theta|D) . However, I cannot find any justification for this. So, why are these Equal?
  45. G

    I Rewriting of equality in conditional probability distribution

    I don't get $$\frac{P[x<X<x+dx|N=n]}{dx}=f_{X|N}(x|n)$$ Can someone derive why? I would believe that $$f_{X|N}(x|n)=\frac{f(x,N)}{p_n(N)}$$ but I don't get how that would be the same. And I don't get that $$\frac{P[x<X<x+dx|N=n]}{dx}=\frac{P[N=n|x<X<x+dx]}{P[N=n]}\frac{P[x<X<x+dx]}{dx}$$ Can...
  46. J

    Probability that a bulb lasts for at least 7 months

    Homework Statement Homework Equations I don't even know how to start this. Should I use Poisson's distribution. Or assume f(x) = exp(-x) And then since mean is given we have integration from 0 to infinite xf(x) is mean. Not sure what this will give. The Attempt at a Solution Let f(x) be...
  47. J

    Probability that both people are from group X

    Homework Statement Homework Equations Probability = number of favourable events / all possible events The Attempt at a Solution Group X Y Total people Indians 10 8 18 (total 18 Indians in both group) Total People 25 20 45 (total 45 people in both...
  48. D

    Probability of spin-flip due to scattering

    Homework Statement A beam of spin-1/2 particles scatters off of a target consisting of spin-1/2 heavy nuclei. The interaction between the particle and nucleus is given by $$V(\vec{ r})= V_0~\delta (\vec{r})~ \vec{S}_1. \vec{S}_2$$ 1) Averaging over initial spin states, find the differential...
  49. jocarren

    I Probability & Time: Is There a Connection?

    Hi, I'm new in the forums, actually I registered to ask this question (I have these wild, often ridiculous ideas). Is there a fundamental relationship betwen the probability of ocurrence of an event and the flow of time around that event? I mean, imagine an isolated space where some type of...
  50. Clifford Engle Wirt

    B Conditional Probability, Independence, and Dependence

    (Mentor note: link removed as not essential to the question.) The problem is: what is relevance anyhow? My questions are these: did I get the math right in the following? Is there a better, more acceptable way to lay out the sample space Ω and the two events F and E? Apart from the math...
Back
Top