What is the definition of probability?

1.	What is the definition of probability?
Answer» If in a random experiment there are n mutually exclusive and equally likely elementary events and m of them are favourable to an event A, then the probability P of happening of A denoted by P(A) is defined as the ratio \(\frac{m}{n}.\) i.e, P(A) = \(\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}\) = \(\frac{n(A)}{n(S)},\) where n(A) = number of sample points in event A n(S) = number of sample points in sample space S. If P(A) = probability of occurrence of A, then P(\(\bar{A}\)) = probability of failure of A or non-occurrence of A = 1 – P(A) as P(A) + P(\(\bar{A}\)) = 1 Note : The probabilities of mutually exclusive and exhaustive events always adds up to 1.

Answer»

If in a random experiment there are n mutually exclusive and equally likely elementary events and m of them are favourable to an event A, then the probability P of happening of A denoted by P(A) is defined as the ratio \(\frac{m}{n}.\)

i.e, P(A) = \(\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}\) = \(\frac{n(A)}{n(S)},\)

where n(A) = number of sample points in event A

n(S) = number of sample points in sample space S.

If P(A) = probability of occurrence of A, then

P(\(\bar{A}\)) = probability of failure of A or non-occurrence of A

= 1 – P(A) as P(A) + P(\(\bar{A}\)) = 1

Note : The probabilities of mutually exclusive and exhaustive events always adds up to 1.

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