Probability basics
What is probability?
Probability is a theory is nothing but common sense reduced to calculation. -Pierre-Simon LaplaceProbability is related to the numerical explanation of how an event can occur, or how true a proposition is.
Experimental Probability is found by repeating an experiment and observing the outcomes.
The Probability of an event always lies between 0 and 1 i.e. (0 ≤ P(E) ≤ 1)
Probability theory, which is widely used in fields such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy.
The book on games of chance book was written by J.Cardon
Random Experiment:An experiment in which all possible outcomes are known and the exact outcome cannot be predicted in advance, is called a Random Experiment.
Example:- Tossing a coin.
- Casting a die.
- Drawing a card from a deck of playing cards.
Outcome: A result of random experiment.
Trail: A trail is a particular performance of a Random experiment.
Event: An event is a collection of a specific outcome or some of the specific outcomes of the experiment. It is a set of all possible outcomes.
Example:If a die rolled, and getting an even number is considered as an event A,then A = {2,4,6}.
Sample space: It is the set of all possible outcomes of a random experiment. Denoted by S
Example:- Toss a coin Sample space, S = {heads, tails} usually write as {H, T}
- Roll a die Sample space, S = {1, 2, 3, 4, 5, 6}
- In tossing two coins , S ={HH,HT,TH, TT}.
Elementary event: An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.
Equally likely event: Something that have the same chance of occurring.
Example:when a die is rolled, the chances of getting an even number or an odd number are the same.
Equally likely events are mutually exclusive to each other.
More likely event: Something would occur with great chance
Certain event or sure event : Something that must occur.
Probability of an Sure event is 1.Less likely event: Some times that occur with less chance.
Impossible event: Something that cannot happen.
Probability of an impossible event is 0.Mutually Exclusive Events: Two or more events of an experiment, where occurrence of an event prevents occurrence of all other events are called Mutually Exclusive Events.
Example:When a coin is tossed, getting head prevents getting tails.
Complimentary Events: Two events are said to be complimentary when one event occurs if and only if the other does not.
We denote ‘not E’ by E̅ this is called the complimentary event of E.DICE:
- It has 6 faces
- On each face have some dots from 1 to 6
Playing cards:
Probability exercise 1 ❯
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