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Probability
Probability is the study of the uncertainty. The uncertainty of any doubtful situation is measured by means of Probability.
Uses of Probability
Probability is used in many fields like Mathematics, Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc.
Key Terms Related to Probability
1. Randomness
If we are doing an experiment and we don't know the next outcome of the experiment to occur then it is called a Random Experiment.
2. Trial
A trial is that action whose result is one or more outcomes. Like –
Throw of a dice
Toss of a coin
3. Independent trial
A trial will be independent if it does not affect the outcome of any other random trial.
Example:
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 will be the collection of some outcomes of that experiment.
Example
If we are throwing a dice then the possible outcome for even number will be three i.e. 2, 4, 6. So the event would consist of three outcomes.
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 D happening is expressed as the following:
Examples
1. If a coin is tossed 100 times out of which 49 times we get head and 51 times we get tail.
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.
Solution
a. Let the probability of getting head is P(H)
b. Let the probability of getting tail is P(T)
c. The sum of two probability is
= P(H) + P(T)
Impossible Events
While doing a test if an event is not possible to occur then its probability will be zero. This is known as an Impossible Event.
Example
You cannot throw a dice with number seven on it.
Sure or Certain Event
While doing a test if there is surety of an event to happen then it is said to be the sure probability. Here the probability is one.
Example: 1
It is certain to draw a blue ball from a bag contain a blue ball only.
This shows that the probability of an event could be
0 ≤ P (E) ≤ 1
Elementary Event
If there is only one possible outcome of an event to happen then it is called an Elementary Event.
Remark
If we add all the elementary events of an experiment then their sum will be 1.
The general form
Example
What is the probability of not hitting a six in a cricket match, if a batsman hits a boundary six times out of 30 balls he played?
Solution
Let D be the event of hitting a boundary.
So the probability of not hitting the boundary will be
So the probability of not hitting the boundary will be 0.8
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