Probability

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1, where, loosely speaking,0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes (“heads” and “tails”) are both equally probable; the probability of “heads” equals the probability of “tails”; and since no other outcomes are possible, the probability of either “heads” or “tails” is 1/2 (which could also be written as 0.5 or 50%).

Types of probability

1) Classical Probability – All sample points have equal chances of the event to happen.
2) Relative frequency- The probability of single data compared to the whole data i.e. possible event to happen relative to all the possible outcomes.
3) Subjectable -Individual, personal judgment to say the probability of the event.

Event is specific collection of sample points

Union
The Union of two events A and B is the event that occurs if either A or B ( or both) occurs on a single performance of the experiment. We denote the union of events A and B by the symbol A Ս B.
Intersection.
The intersection of two events A and B is the event that occurs if both A and B occur on a single performance of the experiment. We write A∩B for the intersection of A and B.
complementary event
The event that does not include all sample points in event
e.g. P(A)+P(AC)=1
P(A)=1-P(AC)

Additive rule of the probability The probability of the union of events A and B is the sum of the probability of events A and B minus the probability of the intersection of events A and B, that is
P(A)+P(B)-P(A and B)

Mutually exclusive  Events: They do not occur at a same time or no common points
P(AUB)= P(A) + P(B)
Conditional probability: If we know the additional knowledge of the probability
P(B/A)=P(A ∩ B)/p(A).