M11. Some basic terms of Probability:

Probability: A type of ratio, which compare how many times an outcomes (results) can occur compared to all possible outcomes (results). 

Probability$(P)$: $\frac{total\; number\; of\; favourable\; cases \;(m)}{total\; number\; of\; cases\;(n)}$      [∵ Click here for more]

1) Experiment:
- A scientific procedure undertaken to make a discovery, test a hypothesis, or demonstrate a known fact. 

The processes, which performs the different possible outcomes (cases) as a result, known as experiment. If the result is not obtained unique, but any one of the possible outcomes. It is called random experiment. 

2) Trial and Events:

Trial: Performing of a random experiment. 

Events: Set of outcomes (results) of an experiments; Important incident (an occurrence). 

3) Exhaustive cases:

An event is said to be exhaustive if we can identify all the possible outcomes. 

Example: In throwing dices, we identify the total number of possible outcomes $(i.e. 1, 2, 3, 4, 5, 6)$ is $6$. Thus the total number of exhaustive cases in rolling a dice is $6$.

4) Equally likely cases:

If any one of the possible outcomes may occur, but no one case can be expected to occur. 

Example: In a rolling dices, there may equally possible to occur a six number $(1, 2, 3, 4, 5, 6)$ marked in the faces of dices.

5) Mutually exclusive cases:

It is not possible to occur all the outcomes at the same time. (OR, If one and only one of them can occur in a single trial).

Example: If we tossing a coin, It is not possible to get both head and tail at a same time. So head and tail are two mutually exclusive events. 

6) Favourable cases:

The happening of an event satisfies the given condition is known as favourable cases. 

Example: In a rolling dice, the cases favourable to getting an even number is $3$ i.e. $(2, 4, 6)$.

7) Dependent cases:

If $A$ and $B$ are two events. Then $A$ affects the probability of the getting of the $B$. It is said to be dependent. (OR, If the occurrence of one event affected by the occurrence of the other).

Example: Imagine, A bag contain $6$ white balls and $4$ red balls. The chance of getting a white ball is $\frac{6}{10}$. If the ball drawn is not replaced and again, we find the probability of getting a white ball is  $\frac{5}{9}$. Hence, probability of getting a $2^{nd}$ white ball depends upon the occurrence of the $1^{st}$ ball.

8) Independent cases:

If $A$ and $B$ are two events. Then $A$ does not affects the probability of the getting of the $B$. It is said to be independent.  

Example: If a coin and dice are rolling, the turning head up in a coin does not affect the getting 6 on the dice.

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