An interpretation of probability is a task of meaning to probability claims. These involve specifying a set of possible cases and defining what a probability claim means in terms of that set.
Understanding Probability Equation is always challenging for me but thanks to all math help websites to help me out.
An interpretation tell us what it means to say that P (p) = r
(Where p can be any sentence and r can be any number between 0 and 1.)
An interpretation must also provide a meaning for conditional probability statements of the form P (p / q) = r.
Interpretations of probability: Over view
Probability ->subjective
->actual degree of belief
->personalist (tempered personalist)
->objective
->classical
->logical
->Frequency
-> Finite freq.
-> Limiting freq.
-> Propensity
Cases of Interpretations of probability:
Classical
Number of possible / total number of possible
Logical
Getting a partially entails, with degree of entailment Finite frequency
Limiting frequency
The limiting frequency in an endless series
Propensity
The limiting frequency of a pair
Interpretations of Probability Example:
What is the probability of getting at least one 6 in two tosses of a die?
Solution:
P (6 on toss 1) = 1/6
P (6 on toss 2) = 1/6
P (6 on both tosses) = 1/36
P (at least one 6 in two tosses) = 1/3
Consider each of the following four bet light (I expect to break even):
1. Pay 36 for [36 if no 6 on 1st toss; 0 if 6]
2. Pay 36 for [36 if no 6 on 2nd toss; 0 if 6]
3. Pay 1 for [42 if 6 on both tosses; 0 otherwise]
4. Pay 12 for [36 if slightest one 6 in two tosses; 0 otherwise]
Algebra is widely used in day to day activities watch out for my forthcoming posts on how to add and multiply fractions and iit jee new pattern 2013. I am sure they will be helpful.
But now consider what happens if I make all four bets:
1st toss 2nd toss Cost Winnings Net gain or loss
6 6 73 72 -1
6 1-5 73 72 -1
1-5 6 73 72 -1
1-5 1-5 73 72 -1
A guaranteed loss!
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