Page 2 - Lesson Notes-Probability

A trial will be independent if it does not affect the outcome of any other random trial.
Like throwing a dice and tossing a coin are independent trials as they do not impact
each other.
4. Event
While doing an experiment, an event is the collection of some outcomes of that
experiment. It is a single result of an experiment.
An event can include one or more possible outcomes.
Example:
• Getting a Tail when tossing a coin is an event.
• Rolling a "5" is an event.
• Choosing a "King" from a deck of cards (any of the 4 Kings) is an event.
• Rolling an "even number" (2, 4 or 6) is also an event.
5. Sample Space
The collection or set of all possible outcomes is called Sample space. It is
symbolically denoted as ‘S’.
Example: For tossing a coin, Sample space (S) = {H ,T}
For throwing a dice, Sample space (S) = {1 ,2,3,4,5,6}

Probability – An Experimental Approach
Experimental probability is the result of probability based on the actual experiments.
It is also called the Empirical Probability.
In this probability, the results could be different, every time you do the same
experiment. As the probability depends upon the number of trials and the number of
times the required event happens.
If the total number of trials is ‘n’ then the probability of event ‘E’ happening is ‘m’.
Then the Probability of the event “E’ is given by

Number of trials in which the event happened
P(E) = =
Total number of trials
Example-1
1. If a coin is tossed 100 times out of which 49 times, we get head and 51 times we
get tail.

a.
a. Find the probability of getting head.
b. Find the probability of getting tail.
c. Check whether the sum of the two probabilities is equal to 1 or not.

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