Page 348 - Start Up Mathematics_8 (Non CCE)

22 Probability

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. To convey probability, terms like
possibility, chance, likely, etc. are also used.
Some common statements used to express probability are:
∑ Virat will probably make a century in this cricket match.
∑ India will possibly become a super power soon.

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 without
actually performing the experiment and based on the previous results.
The main difference between the two approaches is that the theoretical approach is valid 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) 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.
(ii) 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.
(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.
Consider an example of an experiment of tossing a coin. The two possible outcomes are either head (H) or
tail (T).
Let’s now toss two coins simultaneously. There can be the following possible
outcomes: HH, HT, TH, TT. So, the four outcomes are:
Getting head on both the coins (HH)
Getting a head on the first and a tail on the second coin (HT)
Getting a tail on the first and a head on the second coin (TH)
Getting tail on both the coins (TT)
Let’s now toss three coins simultaneously. There can be the following possible
outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.

n
If n coins are tossed simultaneously, then the total possible outcomes are 2 .