Probability

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicate certainty). For example,
1. Probability of raining or not raining on a certain day
2. Probability of a student's passing or not an examination
3. The probability of winning or losing a game etc.

Some of the defined terms used in probability are:

Experiment
Observing the outcomes in probability are experiments. For example, tossing a coin to observe whether head or tail turns up is an experiment.

Random Experiment
If the result of an experiment is not certain, then it is called the random experiment.

Outcome
The result obtained in an experiment is called an outcome.

Sample Space
The set of all possible outcomes of an experiment is called sample space.

Event
Any subset of sample space is called an event.

Sample point
Each result or event of a sample space is called sample point. In tossing a coin, H and T are sample points.

Elementary Point
If the numbers of an event are only one then the event is called elementary point

Equally likely outcomes
If there is an equal chance of getting any outcome of an experiment they are equally likely outcomes.

Favourable outcomes
The outcomes of an experiment whose occurrence show the happening of an event is known as favourable events.

For example in tossing a coin ,
P(H) = \(\frac{n(H)}{n(S)}\) = \(\frac{1}{2}\)

P ({H,T}) = \(\frac{n (HT) }{n(S)}\) = \(\frac{2}{2}\) = 1


General Information of cards, coins and dice on probability:

1. Card

In one packet of the card, there are two colors red and black. Every color has 26 numbers of cards. Red cards are heart and diamond and black cards are spade and club.

In each type of card, there are 1, 2, .......10, J, Q, K which are altogether 13 in number.

Face card: jack (J), queen (Q), and king (K).

In some packets of cards, we find more than 52 cards, which are not necessary for the study of probability.

Drawing a card from the well-shuffled pack of 52 cards, the probability of getting every number is \(\frac{1}{52}\).

2. Coins

There are two possible outcomes while tossing a coin. They are head and tail. When the coin is tossed just once, the probability of getting head or tail is equal.

3. Dice

In a dice, there are altogether 6 faces and when the dice is thrown only once, the probability of occurring a number is 1 to 6 equal.