Probability

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

P(E)

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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