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.
Return to Main Menu