 This 5th grade probability course with definition of a random experiment, outcomes and events is very beneficial. At the end of this chapter, you should be able to calculate a probability in a random experiment.

## I. Randomized experiment

Definition:

The probability of an event is a number, between o and 1, which measures the chances that this event will occur.

Example:

• A coin is tossed: the outcomes are heads or tails.
• We launch the listening of music pieces in random mode among a list of ten titles. The outcomes are the ten titles on the list.
• We try to guess in advance the winner of the soccer world cup among the 32 teams of the final phase. The outcomes are the thirty-two countries in competition.
• A six-sided playing die is rolled. The outcomes are 1,2,3,4,5,6.
Definition:

When the outcomes of a random experiment are all equally likely to occur, i.e. the probabilities of occurrence of the different outcomes are equal, we say that there is equiprobability.

Example:

• We launch the listening of a piece of music in random mode among a list of ten titles. “The piece played is less than three minutes long” is an event.
• We try to guess in advance the winner of the soccer world cup among the 32 teams of the final phase. “The winning country is an African country” is an event. The winning country won its semi-final is a sure event.
• A six-sided playing dice with numbers from 1 to 6 is thrown. “The die falls on an even number” is an event. “The die falls on the number 9” is an impossible event.

## II. probability calculations

Definition:

An experiment is said to be random when we cannot predict what the outcome will be.

The different possible outcomes are called the outcomes of the random experiment.

Definition:

An event is a set of outcomes of a random experiment.

When an event is certain to occur, it is said to be certain.

When there is no chance that an event will happen, it is said to be impossible.

Ownership:

In the case of equiprobability, the probability of an event is obtained by dividing the number of outcomes favorable to the event by the total number of outcomes of the experiment.

Examples:

• A balanced coin is tossed. Each side has as much chance of being obtained as the other. This is a situation of equiprobability. The probability of getting tails is therefore or 50%.
• A classic six-sided, unrigged playing die is rolled. Each side has as much chance of coming out as any other. Of the six sides of the die, three sides have an even number and three sides have an odd number, so the probability of getting an odd number is or 50%.

Remark:

The probability of an impossible event is 0 and the probability of a certain event is 1.

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