Likelihood is the measure of how seemingly an occasion is to occur. It quantifies uncertainty utilizing a quantity between 0 and 1, the place 0 means the occasion is inconceivable and 1 means the occasion is definite.
So if the occasion is about tossing a coin the likelihood of getting heads is:
What’s an Occasion?
An occasion in likelihood is solely an consequence or a set of outcomes of an experiment.
Varieties of occasions
Mutually unique occasions
Two occasions that can’t happen on the similar time are mutually unique.
For instance tossing a coin. Getting a heads and tails in a single toss will not be attainable.
Non — mutually unique occasion
Two occasions are non-mutually unique if they will each happen concurrently.
For instance choosing a card from the deck that’s both a King or Hearts.
Dependent Occasions
When the end result of an occasion impacts the end result of one other occasion then the occasions are dependent.
For instance Drawing two playing cards with out alternative from a deck.
Unbiased Occasions
When the end result of an occasion doesn’t have an effect on the end result of one other occasion then the occasions are unbiased.
For instance tossing two cash. The results of the primary doesn’t have an effect on the second.
Additive Rule
The additive rule of likelihood is used to search out the likelihood of the union of two occasions. It may be expressed as:
- P(A∪B): Likelihood of both occasion A or occasion B occurring (or each).
- P(A): Likelihood of occasion A occurring.
- P(B): Likelihood of occasion B occurring.
- P(A∩B): Likelihood of each occasions A and B occurring
Multiplication Rule
The multiplication rule of likelihood is used to search out the likelihood of the intersection of two occasions.
- P(A∩B): Likelihood of each occasions A and B occurring.
- P(A): Likelihood of occasion A occurring.
- P(B∣A): Conditional likelihood that B happens provided that A has already occurred.
