experimental probability

Examples of experimental probability in the following topics:

• Experimental Probabilities

  • The experimental probability is the ratio of the number of outcomes in which an event occurs to the total number of trials in an experiment.
  • The experimental (or empirical) probability pertains to data taken from a number of trials.
  • $\displaystyle \text{experimental probability of event} = \frac{\text{occurrences of event}}{\text{total number of trials}}$
  • Experimental probability contrasts theoretical probability, which is what we would expect to happen.
  • If we conduct a greater number of trials, it often happens that the experimental probability becomes closer to the theoretical probability.

• Theoretical Probability

  • Probability theory uses logic and mathematical reasoning, rather than experimental data, to determine probable outcomes.
  • Mathematically, probability theory formulates incomplete knowledge pertaining to the likelihood of an event.
  • This probability is determined through measurements and logic, but not through any experimental findings (the future has not yet happened).
  • For example, the probability of rolling any specific number on a six-sided die is one out of six: there are six, equally probable sides to land on, and each side is distinct from the others.
  • This is a theoretical probability; testing by rolling the die many times and recording the results would result in an experimental probability.

• Applications of the Parabola

  • The parabolic trajectory of projectiles was discovered experimentally in the 17th century by Galileo, who performed experiments with balls rolling on inclined planes.
  • Aircraft used to create a weightless state for purposes of experimentation, such as NASA's "Vomit Comet," follow a vertically parabolic trajectory for brief periods in order to trace the course of an object in free fall, which, for most purposes, produces the same effect as zero gravity.

• What is an Equation?

  • For $x + 3 =5$, you have probably already guessed that the only possible value of $x$ is 2, because you know that $2 + 3 = 5$ is a true equation.

• Division of Complex Numbers

  • You are probably already familiar with this concept for ordinary real numbers: dividing by $2$ is the same as multiplying by $\frac12$, dividing by 3 is the same as multiplying by $\frac13$, and so on.

• Circles as Conic Sections

  • You probably know how to find the area and the circumference of a circle, given its radius.

• Polynomial and Rational Functions as Models

  • Of course, this is only possible if the two quantities are related: How many uncles a kid has got has probably nothing to do with how far they can jump.

• Permutations

  • In many calculators, the factorial option is located under the "probability" menu for this reason.

• Rational Algebraic Expressions

  • You could probably find the least common denominator if you played around with the numbers long enough.

• Common Bases of Logarithms

  • The prime number theorem states that for large enough N, the probability that a random integer not greater than N is prime is very close to $\frac {1} {log(N)}$.