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Meaning of Probability
Probability is a chance of occurring in an event from total outcomes. With the help of probability, we can predict the happening of an event. The probability range lies between 0 and 1, where 0 means an impossible event, and 1 means a certain event. More probability, more chance of occurring in an event.
Formula for Probability
Probability of an event P(E)= Number of favourable outcomes/Total outcomes = 0≤P(E)≥1
Example of Probability
There are 12 boys and 4 girls in a class. A student is selected at random. Find the probability of selecting a boy?
Number of boys in class P(B) = 12
Number of girls in class P(G) = 4
Total number of students in class P(B+G) = 12+4 = 16
Therefore, the probability of selecting a boy P(E) = Favourable outcome/ Total outcome
=P(selecting a boy)/P(total students)
= P(B)/ P(B+G)
= 12/16
Terms and definitions used in probability
Sample space- of the possible outcome of a random trial or experiment.b For e.g., tossing a coin {H,T}
Experiment or trial- series of action. For e.g., tossing a coin, rolling a die.
Event- an outcome of an experiment. For e.g., getting a tail after tossing a coin.
Outcome- possible result of an event. For e.g., P(Tail) is a possible result when a coin is tossed.
Complimentary event- non-happening of an event. For e.g., A= getting a tail, whereas complement of event A is not A, it is (A’) = not getting tail.
Impossible event- event that cannot happen. For e.g., getting both head and tail while tossing a coin.
Basic probability rules
Sum of probabilities of all possible outcomes is 1.
For any event A, 0 ≤ P(A) ≤ 1.
Two events that cannot occur at the same time are called mutually exclusive or disjoint events. Probability of occurring either A or B P(A or B) = P(A) +P(B).
P(A or B) = P(A) + P(B) – P(A and B) addition rule.
A and B are Mutually exclusive, then P(A and B) = 0
A and B are not mutually exclusive, then P(A and B) ≠ 0
Complement Rule- P(not A) = 1 – P(A)
P(A or B) = P(event A occurs or event B occurs or both occur)
P(A and B)= P(both event A occurs and event B occurs)
Types of probability
These are 3 main types of probability:
Experimental probability: it is based on the results or observations of an experiment repeated many times. For e.g., a coin is tossed 20 times and got tails 5 times then the experimental probability of getting a tail is-
P(E)= No.of time event occurs/Total number of experiments = 5/20
Theoretical probability: it is based on the reasoning and expectation of happening something. For e.g., a coin tossed, the probability of getting head is-
P(E)= Count of a favourable outcome/Total no. of a possible outcome
Axiomatic probability: it is a set of rules which applies to all types of probability. And these axioms or rules set by the Kolmogorov and are known as Kolmogorov’s three axioms. For e.g., on tossing a coin, the probability of getting head is ½ and tail is ½. Therefore to be an axiomatic probability should satisfy following conditions-
P(E)≥0 (probability of an event is greater than or equal to 0.
P(S) = 1 (probability of sample space is equal to one)
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Conditional probability is based on the occurrence of the previous event or outcome. It is the Probabilities of an event occurring given another event has occurred. You can get conditional Probabilities assignments by high qualified experts at low prices.
In simple words, the probability is the forecasting of future events, while statistics is the analysis of the past event frequency.
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