Equally Likely & Not Equally Likely Outcomes

If all the outcomes of a sample space have the same chance of occurrence, then it is known as equally likely outcomes. It is not necessary that the outcomes are equally likely, but during an experiment we shall assume that the outcomes are equally likely outcomes in many cases.

Equally Likely Outcomes Cases

Equally likely assumptions are applied in the following cases;

1. Playing a Card: In a deck, there are 52 ordinary playing cards. In this all 52 cards are of the same size and therefore, it is assumed as equally likely outcome of each card i.e., 1/52
2. Tossing a Coin: During tossing a single coin, there are two possible outcomes i.e., head and tail. It is always assumed that both are equally likely and each has a chance/probability of occurrence 1/2. If not, then the criteria should be mentioned. In case of tossing more than one coin it is assumed that on all the coins, head and tail are equally likely.
3.  Throwing a Dice: There are six “6” possible outcomes when rolling a single dice. In this case all the six outcomes are assumed to be equally likely outcome. Each has a probability of occurrence 1/6.
4. Drawing Balls From a Bag: This is the last case in which probability of occurrence is assumed as equally likely. For example a ball is selected randomly from a bag having balls of different colors. In this case it is assumed that each ball in the bag has an equal outcome.

Not Equally Likely Outcomes

When a sample space consists of outcomes that don’t have an equal chance of occurrence, then the resultant outcomes are said to be not equally likely outcomes.

Examples of Not Equally likely outcomes

1. A matchbox has six “6” face, but all the faces not equally likely. Therefore, probability of occurrence of each face varies. Each face has different occurring value.
2. A bag is full of balls having different colors and sizes. Now pick up a ball randomly from the bag. The probability of all the balls will not be the same. Probability of occurrence of each ball will vary.