What is Probability? — Mathematics

Definition 71.5 Primary & Middle School Mathematics · Chapter 71 — Statistics and Probability

A random experiment has several possible outcomes; an event is a set of outcomes. Each outcome gets a probability: a number between $0$ and $1$ , with all the probabilities of the outcomes summing to $1$ ; the probability $\P(A)$ of an event $A$ is the sum of the probabilities of its outcomes. When all $n$ outcomes are equally likely,

\P(A) = \frac{\text{number of favorable outcomes}}{n}.

Examples

Example 71.6

A wheel is split into $8$ equal sectors: $3$ red, $3$ blue, $2$ green. Each sector has probability $\frac18$ , so

\P(\text{red}) = \frac38, \qquad \P(\text{green}) = \frac28 = \frac14, \qquad \P(\text{not green}) = 1 - \frac14 = \frac34 .

Example 71.9

A bag holds $2$ red and $3$ black tokens. Draw one token, note its color, put it back, draw again. Each draw gives red with probability $\frac25$ , black with probability $\frac35$ .

The tree of the two draws with replacement: multiply along the branches, and check that the four paths sum to 1. — The tree of the two draws with replacement: multiply along the branches, and check that the four paths sum to $1$ .

Probability of two tokens of the same color: $\frac{4}{25} + \frac{9}{25} = \frac{13}{25}$ . Probability of at least one red: $1 - \P(\text{BB}) = 1 - \frac{9}{25} = \frac{16}{25}$ .

Read in context →

Examples

Related terms