What is Probabilities: Definition and 396 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.

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  1. C

    Multiplying the probabilities of two disjoint sets.

    I've been struggling for a few minutes with this basic thing and I want to make sure I got it right, given A, B being disjoint, We know that P(A and B) = 0 However, if they are independent then P(A and B) = P(A) x P(B) Then if P(A) is finite non zero and P(B) is finite non zero, how...
  2. M

    MHB Calculating Probabilities with Spinner Outcomes: One Way or Another

    A spinner has three possible outcomes which occur with probabilities a, b and c where a+b+c=1. What is the expected number of spins required until all three outcomes are seen? There's an easy way and a harder way to do this. Guess which I did first.
  3. C

    Thought process improvement on Probabilities

    I had a problem that said "I throw nine balls randomly in five containers. What's the probability any container will have exactly five balls by the end of the process?" The answer involved using a Binomial distribution. Now the question is, how do I train my mind to go to the use of...
  4. J

    Lottery Probabilities With Supplementary Numbers

    Hi All, I'm trying to figure out the probability of winning the lotto. 8 numbers are drawn between 1 and 45. The first six are 'winning' numbers, the last two are the 'supplementary' numbers. To win division 1, you need to get all six winning numbers right: \binom {45}6 = 8145060 Hence...
  5. M

    PBR Paper, Calculation of Outcome Probabilities

    I'm trying to understand the PBR proof as explained in their paper on arXiv (http://arxiv.org/abs/1111.3328). I'm having trouble following the calculation of the probability of measurement outcomes on page 6 (A7). Specifically, going from the first line to the second line of A7, they seem to...
  6. P

    Probabilities inequalities

    the random value X has the inequality , -10<=X<=10 and E(X)=2, what is the minimum upper bound of the probability P(X>=5) ? my first thought was to find this P(X>=t)<=E(X)/t which is 2/5 from Markov but its not correct, any ideas?
  7. G

    S1 Probabilities P(A' u B)

    Hi all, Could you confirm this for me please. I am revising S1 statistics. P(A' u B) = P(B) + P(A' u B') Is that true? I assume you can represent that on a venn diagram. Is that true. I am having trouble understanding the equations which contain ' such as P(A' n B). Thank you.
  8. P

    Expectanion value probabilities

    Flipping a coin 10 times. The currency brings crown with probability 0.57. If you bring a total of k heads they add 2 ^ k euros. What is the average profit in this game? i must find the expectanion value and i do this: ∑from k=1 to 10 --->((0.57)^k)*(2^k) =22.0445164 i think that my...
  9. C

    Explaining P(k)=c(101-k) for Finding 'c' in Turtle's Life Expectancy

    That's not exactly coursework (it's studying) but I've spammed the probabilities forum too much. Can someone explain this part? Knowing that P(k)=P(X=k)=c(101-k) For a 'turtle' that can live up to 100 years, find 'c'. And it goes I don't understand the jump from cΣk to...
  10. F

    Using MATLAB to work out coin-flip style probabilities

    I've basically been set the task below however I've not really been taught how to go about it. I think I know the general theory of how to go about it but the actual commands and putting it all together bamboozles me. The question is attatched. Just seen the typo, it should be 'loses' not...
  11. X

    Energy probabilities of the harmonic oscillator

    Homework Statement A particl of mass m in the potential V(x) (1/2)*mω^{2}x^{2} has the initial wave function ψ(x,0) = Ae^{-αε^2}. a) Find out A. b) Determine the probability that E_{0} = hω/2 turns up, when a measuremen of energy is performed. Same for E_{1} = 3hω/2 c) What energy...
  12. J

    Question about probabilities with playing cards

    Let's say that I'm playing a card game with 3 friends. The game involves a full deck of regular playing cards (52 cards, 4 suits, etc.) For this game, each player is dealt 5 cards. The cards are dealt out 5 cards at a time and in a clockwise direction starting with the person to the left of the...
  13. O

    Calculate Temperature of reservoir from microstate probabilities

    Homework Statement Consider a network of N = 1006 non-interacting spin 1/2 particles fixed to the sites of a 1D lattice. The network is placed in an external uniform magnetic field so that its total (fixed) energy is given by E = -(N up- N down)ε = -100ε where ε is a positive constant...
  14. J

    Probabilities of archers A and B hitting the bull's eye

    Homework Statement Two archers A and B take turns to shoot, with archer A taking the first shot. The probabilities of archers A and B hitting the bull's eye is 1/6 and 1/5 respectively. Show that the probability of archer A hitting the bull's eye first is 1/2. Homework Equations...
  15. S

    Normalising and Probabilities of wavefunctions

    Hey My question is displayed below I think I have done this right but I wanted to check, we have to normalise the wavefunction first and I think this is done by assuming each state is equally likely and so assigning some constant 'c' to premultiply each of the 3 states. We need...
  16. J

    Solve Card Probability: King of Hearts in Deck

    I need some help solving this homework problem. If you were to randomly select a card one at a time without replacement from a shuffled deck until only face cards remain in the deck, what is the probability that the king of hearts remains in the deck? Assume there are 16 face cards in a 52 card...
  17. J

    Projecting Win Probabilities in Fantasy Sports

    So, I made it to the finals for my fantasy football league. The winner receives $100 and the runner-up $10 (maybe disregard this runner-up reward for simplification). I wanted to know how to calculate an offer to both teams, based upon the probability of winning, such that any risk-neutral...
  18. A

    Probabilities from movie 21

    This is the problem that a teacher (Kevi Spacey actually) presented the class on the movie 21: You are on a TV show and the announcer asks you to choose 1 from 3 doors. Behind 2 doors there are a goat and behind 1 there is a new car. The guy coose door 1. The announcer go and opens door 3...
  19. W

    Statistics Problem regarding conditional probabilities

    Homework Statement A certain delivery service offers both express and standard delivery. Eighty-five percent of parcels are sent by standard delivery and 15% are sent by express. Of those sent standard, 80% arrive the next day, and of those sent express, 95% arrive the next day. A record of...
  20. fluidistic

    Probabilities: System reliability

    Homework Statement I must show that the conditional density of probability P(t|\tau )dt that a device fails between time t and t+dt given that it has no failed up to time \tau is P(t|\tau )=\frac{P(t)}{S(\tau )}; where P(t)dt is the density of probability that the device will fail between...
  21. T

    Reverse Conditional Probabilities

    I've written a modified mutation algorithm that I am trying to derive a more analytical probability model for. The basic algorithm works like this: 1. The probability of mutation is P(M) = 0.01. 2. If mutation occurs, then: a. The probability that mutation-type A is P(A|M) = 0.50 b. The...
  22. A

    Time-Dependent Perturbation Theory and Transition Probabilities

    I'm rather stuck on this problem. I seem to be having issues with the simplest things on this when trying to get started. Homework Statement There is a particle with spin-1/2 and the Hamiltonian H_0 = \omega_0 S_z. The system is perturbed by: H_1 = \omega_1 S_x e^{\frac{-t}{\tau}}...
  23. J

    Quantum Computation Probabilities

    Homework Statement Let a one-qubit system be in the state \left|ψ\right\rangle = \frac{\sqrt{15}\left|0\right\rangle + i\left|1\right\rangle}{4}. If we perform a measurement to see whether the qubit is in the state \left|x_{+}\right\rangle = \frac{\left|0\right\rangle +...
  24. J

    Comp Sci Calculating Probabilities in C++

    Homework Statement Working on a program that will calculate the results of a shootout between 3 people, each of whom have a different level of accuracy (one hits his mark 1/3 of the time, one hits his mark 1/2 of the time, one hits his mark 1/1 of the time). Homework Equations...
  25. L

    Calculating Probabilities for Studying Hours in Multiple Subjects

    Suppose a student has 15 hours to study for exam in 5 subjects. She puts 15 plain and 4 chocolate mini candy bars into a paper bag and starts studying the first subject. At the end of every hour, she pulls a candy bar at random from the bag. If it is plain, she eats it and continues to study the...
  26. P

    Taking a mean average of two probabilities to predict an outcome?

    I hope this the right place to ask this question. I appologize if this is in the wrong place. I am not from a probability background. I have tried to search for an answer to my question, but I have not found it in any of the literature which I can understand. I'm not even sure exactly how to...
  27. C

    Understanding Conditional Probabilities

    Homework Statement Suppose you have 3 nickels and 4 dimes in your right pocket and 2 nickels and a quarter in your left pocket. You pick a pocket at random and from it select a coin at random. If it is a nickel, what is the probability that it came from your right pocket? 2. The attempt at a...
  28. Physics Monkey

    Truncating probabilities based on entropy

    Roughly speaking, I want to know how badly Shannon can fail in the one-shot setting. The standard ideas of asymptotic information theory give a precise meaning to the entropy of a given probability distribution in terms of best achievable compression with vanishing error in the limit of many...
  29. J

    Probabilities of quantum states

    In measuring the x component of angular momentum of a state, by using the expectation value calculation of Lx, i got i/3 h bar - i/3 h bar, does this means that the probability of h bar is i/3 and the probability of 0 h bar is 0 and the probability of -h bar is i/3? If so, when is the...
  30. N

    Unconditional probabilities do not exist? Discuss

    I am somewhat annoyed by the term "unconditional probability", in that all probabilities are indeed conditional on filtration (an information set if you would like), without which, a probability is inadequately defined as though plucked out of thin air based on no logical information. I make...
  31. M

    A) Investigating Probabilities of X < 1

    1) (1 pt) You are investigating a random phenomenon and have determined that the cumulative distribution function F_{X}(x):=P(X<x) of the random variable X has values F_{X}(1)=.5, F_{X}(2)=.74, F_{X}(3)=.92 A) Less than 1 _____ B) Larger than 2 _____ C) Between 1 and 3 _____ 2)...
  32. M

    Order Statistics Probabilities

    Homework Statement Let Xi ~ iid f(x) = (2x)I[0,1](x), i = 1,...,n. Find the distribution of X(1). What is the probability that the smallest one exceeds .2?
  33. mcknia07

    What is the product of these two probabilities

    Took Drug Didn't Total Cholesterol ≤ 200 60 50 110 Cholesterol > 200 40 50 90 100 100 200We’ll call event A “cholesterol ≤ 200” and event B...
  34. T

    Decompostion of conditional probabilities

    So If B=B1UB2U...UBn would Pr(A|B)=Pr(A|B1)Pr(B1)+Pr(A|B2)Pr(B2)+...+Pr(A|Bn)Pr(Bn)? I haven't found a formula for this but it makes intuitive sense.
  35. rcgldr

    Probabilities, 7 items, 4 containers

    Starting a new thread to avoid hi-jacking my previous thread: https://www.physicsforums.com/forumdisplay.php?f=73 There are 7 items, and 4 containers. A 4 sided die (tetrahedron) is used as a random number generator and is thrown 7 times. After each toss, an item is dropped into a...
  36. S

    Technical difficulties in calculating hydrogen probabilities

    I am trying to prove to myself that the most probable distance for a 1s electron in a H atom is the Bohr radius. The probability of finding an electron (for any given state in a hydrogenic atom) in a spherical shell of thickness dr at a distance r from the nucleus is \left|R_{nl}\right|^{2}...
  37. K

    Regarding BEC: Bose distribution and probabilities

    Hello PF. I won't just lurk around today, I will pose a question. I was looking at a dilute ultracold bosonic gas and was trying to see how one can predict the existence of a BEC and got stuck on this: I was comparing probabilities between finding the system in the lowest state...
  38. G

    Understanding Markov Chains: Deriving and Solving Probabilities

    Hello all I have a question about Markov chain I've obtained in an application. There is no need to mention the application or the details of markov chain because my question is simply: The transition probabilities are derived with equations that depend on the stationary probability, I know...
  39. A

    Calculating Hybrid Probability When Two Probabilities Affect the Same Event

    Calculating "Hybrid Probability" When Two Probabilities Affect the Same Event In this "minesweeper grid:" http://a1.sphotos.ak.fbcdn.net/hphotos-ak-snc7/401541_958641223250_10904138_40885678_1330475914_n.jpg ...I can calculate the probability of the square with the question mark being a...
  40. N

    Limits involving logs, negative inf and probabilities.

    Hello! I am playing around with an equation (i.e. it's not a textbook question), and I arrived at the following problem: The equation is: A = -1*\sum_{i=1}^{N}*\log_{N}(P_{i})*P_{i} Pi is less than or equal to 1 and more than or equal to 0, and is a probability of finding an object in a...
  41. J

    Why 8 probabilities in 3D random walk?

    Why are there 8 possible moves in 3D random walk? With R being the distance from the origin, how is its relationship with the number of steps and dimensionality? Thx!
  42. StevieTNZ

    Can A Single Photon Be Split Into 45 and 135 Degree Polarization?

    Really two questions: 1. In the Do-It-Yourself Quantum Eraser article written by Rachel Hillmer and Paul Kwiat (published in Scientific American, May 2007), on page 93 there are instructions to cut in half horizontally a D-orientated (45 degrees clockwise from V), and an A-orientated (45...
  43. S

    Probabilities with infinities

    A probability of zero for an event says that it is impossible right?Then let's say that I need to choose a number randomly among the infinite numbers between 2 and 5.The probability of picking a particular number should be zero.And yet i can pick a number randomly(whose probobility of being...
  44. W

    Probabilities with Chips and Bowls

    A better way to do Probabilities with Chips and Bowls? Question: bowl 1 contains 6 red chips and 4 blue chips. 5 chips are selected at random and placed in bowl 2. then 1 chips is drawn from bowl 2. Relative to the hypothesis that this chip is blue, find the conditional probability that 2 red...
  45. StevieTNZ

    Verification of probabilities for various states

    The experimental team takes a sample of the population to probe. I know QM can predict an expectation value for observable A. When the results are returned, there is an experimental value +/- uncertainty. For a verification, would the result need to concide with the expectation value? Would...
  46. J

    The Gauge Dependence of Quantum Transition Probabilities

    I was trying to understand the standard calculation of Einstein's A,B coefficients in quantum theory textbooks and I came across the following difficulty. In the calculation of transition probabilities, total wavefunction is expanded into eigenstates of time-independent H_0 and the expansion...
  47. T

    Conditional Probabilities problem

    1. Homework Statement ******* SOLVED ********* There are three magazines A,B and C respectively. A survey of readers was taken and the following data was collected. 0.6 Read A 0.5 Read B 0.5 Read C 0.3 Read A&B 0.2 Read B&C 0.3 Read A&C 0.1 Read A&B&C What is the probability that a reader...
  48. StevieTNZ

    Probabilities in Quantum Mechanics

    Hi there, The average expected result for particles with 1/2 probability going through slit 1 and 1/2 probabiltiy going through 2, for a large number of particles (N) is exactly that: 1/2 slit 1, 1/2 slit 2. We send the large number of particles through and find that roughly half go...
  49. J

    Probabilities of Random Guessing

    Hello, I am a student in high school and I possesses a keen proclivity for mathematics and physics. A contentious topic of discussion has come up among my friends, and I seek some assistance in resolving it. A few days ago in my AP Chemistry class, the instructor told us that were we to...
  50. S

    Probabilities and binomial theorem

    Homework Statement Consider an ideal gas of N identical particles in a volume V, and a subvolume v. The chance a molecule is in inside the subvolume is P = v/V. a) What is the chance the subvolume contains n particles? b) Use the binomial theorem (p + q)^N = \sum_{n = 0}^N p^n q^{N-n}...
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