Probability and It’s Charecteristics

Probability is a numerical measure of the likelihood that a specific event will occur.

There are two properties of probability. The explanation are given bellow-

First Property: The probability of an event always lies in the range 0 to 1.

It simply means that, whether it is simple or a compound event, the probability of an event is never less than zero or greater than one.

Mathematically implies that-

0 ≤ P(E_i) ≤1; For Simple event

0 ≤ P(A) ≤1; For Compound event

What does mean impossible event or sure event?

An event that can not occur has zero probability; such an event is called an impossible event. For example: If we roll a die, we will never get number 7 and the probability of showing up number 7 is '0'.

An event that is certain to occur and the probability is equal to 1 is called a sure event.

For example: Universal truth event.

Mathematically implies that-

For an impossible event M: P(M)=0

For a sure event C: P(C)=1

Second Property:

The sum of the probabilities of all simple events for an experiment is always 1.

Mathematically implies that-

∑P(E_i)=P(E₁)+P(E₂)+P(E₃)+…..=1

For example:

For the experiment of one toss of a coin.

P(Head)+P(Tail)=1

What does mean the valid or invalid probability?

For a valid probability distribution, an event must be follow the two charecteristics of probability as i mentioned above.

For an invalid probability distribution, an event either follow any one charecteristics or doesn't follow or maintain the two properties of probability.

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