The outcomes of a sample space are called equally likely if all of them have the same chance of occurring. It is very difficult to decide whether or not the outcomes are equally likely, however in this tutorial we shall assume in most of the experiments that the outcomes are equally likely. We shall apply the assumption of equally likely in the following cases.
(1) Tossing a coin or coins
When a coin is tossed, it has two possible outcomes called heads and tails. We shall always assume that heads and tails are equally likely if not otherwise mentioned. For more than one coin, it will be assumed that for all the coins, heads and tails are equally likely.
(2) Throw of a die or dice
Throwing a single die can produce six possible outcomes. All six outcomes are assumed equally likely. For any number of dice, the six faces are assumed equally likely to be produced.
(3) Playing cards
There are 52 cards in a deck of ordinary playing cards. All the cards are of the same size and are therefore assumed equally likely to be chosen.
(4) Balls from a bag
There are many situations in probability in which some objects are selected from a certain container. The objects in the container are assumed to be equally likely to be chosen. A famous example is the selection of a few balls from a bag containing balls of different colors. The balls in the bag are assumed equally likely to be selected.
Not Equally Likely Outcomes
When all the outcomes of a sample space do not have an equal chance of occurring, the outcomes are called not equally likely. When a matchbox is thrown, all six faces are not equally likely to come up. If a bag contains balls of different sizes and a ball is selected at random, all the balls are not equally likely to be selected.