probability

Examples of probability in the following topics:

• Experimental Probabilities

  • 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.
  • In statistical terms, the empirical probability is an estimate of a probability.
  • An advantage of estimating probabilities using empirical probabilities is that this procedure includes few assumptions.
  • Intuitively we know that the probability of landing on any number should be equal to the probability of landing on the next.

• 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.
  • As such, the meteorologist's 60% verdict is a theoretical probability, and not the result of any proven experiment.
  • 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.

• 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.

• What is an Equation?

  • 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.

• 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.

• 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 $\frac {1} {log(N)}$.

• Rational Algebraic Expressions

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