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Consider an experiment of tossing a coin. Before tossing a coin, we are not sure whether head or tail will come up. To measure this uncertainty, we will find the probability of getting a head and the probability of getting a tail.

A student tosses a coin 1000 times out of which 520 times head comes up and 480 times tail comes up.

The probability of getting a head is the ratio of the number of times head comes up to the total number of times he tosses the coin.

Probability of getting a head

= 0.52

Similarly, probability of getting a tail

= 0.48

These are the probabilities obtained from the result of an experiment when we actually perform the experiment. The probabilities that we found above are called experimental (or empirical) probabilities.

On the other hand, the probability we find through the theoretical approach without actually performing the experiment is called theoretical probability.

The theoretical probability (or classical probability) of an event E, is denoted by P(E) and is defined as


Here, we assume that the outcomes of the experiment are equally likely.

When a coin is tossed, there are two possible outcomes. We can either get a head or a tail and these two outcomes are equally likely. The chance of getting a head or a tail is 1.

Thus, probability of getting a head P(E)

Similarly, probability of getting a tail =

Here, (or 0.5) is the theoretical probability. 

Now, in order to understand this concept in greater detail, let us take a look at the following video.


Relation between Experimental and Theoretical Probabilities:


There is a fact that the experimental probability may or may not be equal  to the theoretical probability.

For example, if we take a coin and toss it by a particular number of times then the theoretical probab...

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