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Probability

In our daily life, we come across many statements like:

1. He might come today.
2. My mother was doubtful whether to cook non-vegetarian food or not.
3. Chances are very high that the war will take place.

In all these statements, we are not sure about the occurrence of the events. There is an element
of uncertainty related to these statements. The words might, doubtful, chances, etc. show either
the uncertainty or the probability of an event.

Probability is the chance, likelihood, or possibility of the occurrence of an event. It is used on
large scale in science, forecasting weather, commerce, etc.
Thus, probability is defined as the measure of the likelihood of something happening.

Important Terms Related to Probability

Some important terms used in probability are defined as below:
1. Random Experiment: An action that cannot perform the exact outcome in advance is called
a random experiment.
For example, when a die is rolled, we already know that any of the numbers from 1 to 6
could turn up, but which number will turn up is not certain.
2. Outcome: The result of a single trial of an experiment is called the outcome. For example,
the appearance of 1, 2, 3, 4, 5, and 6 on rolling a die are the outcomes.
3. Event: An action that produces a definite result is called an event. For example, tossing a
coin or rolling dice is an event. Some events cannot occur. For example, getting a number 7
when a die is rolled is impossible. Such events are called impossible events. The probability
of an impossible event is 0.
Some events surely happen. For example, all students of class VII aged less than 25 years
are sure. Such events are called sure events. The probability of a sure event is 1.
4. Equally Likely Outcomes: What is the likelihood of getting a head or a tail when an unbiased
coin is tossed once. Each of the two outcomes has an equal chance of occurring. This is
called equally likely events.
5. Sample Space: The list of all possible outcomes is called sample space and is denoted by S.
For example, when a dice is rolled, the possible outcomes are 1, 2, 3, 4, 5, and 6. So, the
sample space S = {1, 2, 3, 4, 5, 6}.
Experiment 1: Toss a coin once.
When we toss a coin once, all the possible outcomes will be either Head or
Tail, i.e., {H, T}.
Experiment 2: Toss two coins together.
When we toss two coins together, all the possible outcomes will be two heads,
two tails or one head and one tail i.e. {HH, TT, HT, TH}.

number of times the event E occurs
So, we define probability of an event E, P(E) =
total number of trials

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