Page 267 - ICSE Math 8

24 Probability

Key Concepts

• Theoretical Approach to Probability • Deck of Playing cards
• Tossing One, Two or Three Coins • Theoretical Probability
• Throwing a Die Twice

You are familiar with the concept of probability which was introduced to you in the previous class. Probability
is the study of the likelihood or chance of the occurrence of a given event. It is a number expressing the ratio
of likely outcomes to the total number of possible outcomes. Terms like possibility, chance, likely, etc., are
used to express probability.
Some common statements used to express probability are:
• Virat will probably make a century in a particular cricket match.

• India will possibly become a super power soon.
• There may be a duststorm in the evening.

Theoretical Approach to Probability

You have already learnt about experimental or empirical approach to probability in the previous class. This
approach emphasizes on the probability of an event based on the actual occurrence.

Let’s learn the theoretical approach to probability where the emphasis is to predict the future occurrence of an
event without actually performing the experiment and also without using the previous results.

The main difference between the two approaches is that the theoretical approach is based on the assumption
that the number of trials of an experiment is very large whereas in experimental approach it is smaller.
Some important terms associated with probability are:

(i) Experiment: An experiment is an action which results in well-defined outcomes.
(ii) Deterministic operations: The experiments which produce identical results or outcomes on several
repetitions, if the conditions are identical are called deterministic operations (experiments). For example,
the chemical experiments you perform in your school laboratory repeat the same outcome under identical
conditions.
(iii) Random (or Probabilistic) experiment: An experiment in which all possible outcomes are known but
the exact outcome cannot be predicted in advance is called a random (or probabilistic) experiment.
For example, in an experiment of tossing a coin, all the possible outcomes, i.e., head or tail are known,
but it is impossible to predict which outcome will eventually happen.
Let’s now learn about various terms associated with the random experiment.
(a) Outcome: A possible result of a random experiment is called its outcome. Outcomes are said to be
equally likely if there are equal chances of each outcome to take place. For example, a coin can have
only 2 outcomes, i.e., head or tail and they are equally likely.
(b) Trial: Performing a random experiment is called a trial.
(c) Event: An event is one or more outcomes of a random experiment. It is infact a part of all possible
outcomes. An event can be a sure or an impossible event. In throwing a die, an event of getting
a natural number upto 6 is a sure event. Getting a number more than 6 is an impossible event.

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