Terminology Related to Chance and Probability

Some fundamental concepts associated with probability are explained below, students are advised to read all the points in detail to get a complete idea about probability.

• Experiment: A trial in which some well-defined outcome is expected is called an experiment.  
• Outcome: The result of an experiment is called outcome. For example, head/tail are possible outcomes while tossing a coin.
• Sample Space: A set of all possible outcomes is called sample space. For example, while tossing a coin, sample space S is

S = {H, T}, where H refers to the Head and T refers to the Tails

• Random Experiment: A random experiment is an experiment whose outcome may not be predicted in advance. It may be repeated under numerous conditions. Some examples of random experiments are,
  • Tossing a Coin – Head and tails are the possible outcomes.
  • Rolling a Dice – There are six possible outcomes, 1, 2, 3, 4, 5, and 6.  
• Equally Likely Outcomes: The equally Likely Outcomes refers to a condition when each outcome of an experiment is equally likely. In other words, each outcome has the same chance of occurring. For example, while tossing a fair coin, there are equal chances to get a head or a tail.
• Likely chances to probability: Let us consider the following cases to understand likely chances to probability.

Case 1: Tossing a coin

While tossing a coin, the sample space = {H, T}. There are two possible outcomes Head and tail, since both outcomes are equally likely, we can conclude that the likelihood of getting head = 1/2. Similarly, the likelihood of getting a tail = 1/2

Case 2: Rolling a Dice

Sample space = {1, 2, 3, 4, 5, 6}

Total possible outcomes = 6

Since all outcomes have an equal chance, so the likelihood of occurrence of each outcome = 1/6

• Outcomes of Events: The occurrence of each outcome in an experiment forms an event. For example, in the experiment of tossing a coin, the occurrence of the head, as well as the occurrence of a tail, are considered events.
• Impossible Events: When the probability of an event is 0, then the event is known as an impossible event. An example of an impossible event is, “The Sun Rises in the West.”
• Sure Events: When the probability of an event is 1, then the event is known as a sure event. An example of the sure event is, “The Sun Rises in the East.”

Chance is defined as the natural occurrence of any event without any interference, we can also say that the possibility of any event is the chance of the event, and mathematically we define the chance as the probability of an event.

Probability refers to the likelihood of the occurrence of an event. The event may or may not occur. For example, we have some of the real-life statements which we hear in our daily lives:

• My uncle may visit us today
• There is a good chance that it may rain tomorrow
• The school may probably take us to a picnic in June
• Schools may reopen in March

These daily life statements use terms like ‘probable’, ‘may’, ‘has a good chance’, ‘likely’ etc., so it is clear that there is no surety of occurrence, it may occur, or it may not occur, so this is called chance. In other words, a chance is a possibility of something happening. And in mathematics, probability is known as chance. Chance and Probability is an important topic for Class 7 and Class 8 students.

In this article, we will learn about, Chance, Probability, Formula of Probability, and others in detail. The concepts of probability are frequently used in Statistics, engineering, data science, and hypothesis testing.