Page 13 - Probability Demystified

2 CHAPTER 1 Basic Concepts

Probability Experiments

Chance processes, such as flipping a coin, rolling a die (singular for dice), or
drawing a card at random from a well-shuffled deck are called probability
experiments.A probability experiment is a chance process that leads to well-
defined outcomes or results. For example, tossing a coin can be considered
a probability experiment since there are two well-defined outcomes—heads
and tails.
An outcome of a probability experiment is the result of a single trial of
a probability experiment. A trial means flipping a coin once, or drawing a
single card from a deck. A trial could also mean rolling two dice at once,
tossing three coins at once, or drawing five cards from a deck at once.
A single trial of a probability experiment means to perform the experiment
one time.
The set of all outcomes of a probability experiment is called a sample
space. Some sample spaces for various probability experiments are shown
here.

Experiment Sample Space
Toss one coin H, T*
Roll a die 1, 2, 3, 4, 5, 6
Toss two coins HH, HT, TH, TT
*H = heads; T = tails.

Notice that when two coins are tossed, there are four outcomes, not three.
Consider tossing a nickel and a dime at the same time. Both coins could fall
heads up. Both coins could fall tails up. The nickel could fall heads up and
the dime could fall tails up, or the nickel could fall tails up and the dime
could fall heads up. The situation is the same even if the coins are
indistinguishable.
It should be mentioned that each outcome of a probability experiment
occurs at random. This means you cannot predict with certainty which
outcome will occur when the experiment is conducted. Also, each outcome
of the experiment is equally likely unless otherwise stated. That means that
each outcome has the same probability of occurring.
When finding probabilities, it is often necessary to consider several
outcomes of the experiment. For example, when a single die is rolled, you
may want to consider obtaining an even number; that is, a two, four, or six.
This is called an event. An event then usually consists of one or more