Equally Likely Outcomes

The outcomes of a sample space are called equally likely if all of them have the same chance of occurrence. It is very difficult to decide whether or not the outcomes are equally likely. But 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) Throw of a coin or coins:

When a coin is tossed, it has two possible outcomes called head and tail. We shall always assume that head and tail are equally likely if not otherwise mentioned. For more than one coin, it will be assumed that on all the coins, head and tail are equally likely.

(2) Throw of a die or dice:

Throw of a single die can be produced six possible outcomes. All the six outcomes are assumed equally likely. For any number of dice, the six faces are assumed equally likely.

(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.

(4) Balls from a Bag:

There are many situation in probability in which some objects are selected from a certain container. The objects of the container are assumed to be equally likely. A famous example is the selection of a few balls from a bag containing balls of different colors. The balls of the bag are assumed equally likely.

Not Equally Likely Outcomes:

When all the outcomes of a sample space do not have equal chance of occurrence, the outcomes are called not equally likely. When a matchbox is thrown, all the six faces are not equally likely. If a bag contains balls of different sizes and a ball is selected at random, all the balls are not equally likely.