Published by: sadikshya
Published date: 13 Jun 2021
The following are the approaches to probability:
If there are ‘n’ mutually exclusive and mutually likely cases and ‘m’ of them are favorable to an event ‘E’. Then, the probability of the happening of an event ‘E’ denoted by probability is given by:
Remarks:
ie.
p + q = 1
If A and B are two events with their respective probabilities P(A) and P(B) then the probability of occurrence at least one of these two events given by:
where P(A U B) is the probability of the simultaneous occurrence of events A and B.
Remarks:
1. If A & B are mutually exclusive event then,
2. If A & B & C are 3 events then the ‘P’ of occurrence of at least one of these events is given by:
If A & B & C are mutually exclusive then, the probability is
If two events A & B are independent then the probability of their simultaneous occurrence is equal to their individual probabilities. If P(A) and P(B) be the probabilities of occurrence of events A & B respectively then the probability of their simultaneous occurrence is given by:
Remarks:
where,
is the probability of occurrence of event B given that A has already occurred.
A | B | Total | |
C | N1 | N2 | N1 + N2 |
D | N3 | N4 | N3 + N4 |
Total | N1 + N2 | N2 + N4 | N |
The probability of each event given by a row or column in the contingency table is called marginal probability.
The marginal probabilities are:
The probability of the joint event whose frequency is given in the cells in the table is called joint probability.
The joint probabilities are: