Today is our topic of discussion Data Based Probability.
Data Based Probability
In the logical approach to determining probabilities, the outcomes are required to be equally likely. However, in reality the outcomes are not equally likely in all cases. Moreover, in many situations, it is not possible to apply the logical approach. For example, today’s weather forecast says that the probability of raining today is 30%, the probability of Brazil winning the world football cup is 40%, the probability of Bangladesh winning the Asia cup is 60%. Then statement are based on statistics or data of past records and this is the concept of data-based probability.
Suppose, a coin is tossed 1000 times which resulted in head 523 times. So the 523 relative frequency of getting head is 0.523. Suppose, a coin is tossed 2000 1000 times which resulted in head 1030 times. So the relative frequency of H in 2000 times is 1030 2000 0.515. From this we can understand that, the more times an experiment (tossing of a coin) is done, the closer the relative frequency will be to the probability of getting a head in a single tossing of the coin. This is called data based probability.
Determination of Probability using Sample Space and Probability Tree
It has been already mentioned that the set of all possible outcomes of an experiment is called the sample-space. Often the sample space of an experiment is quite large. In such cases, the counting of all sample points and the formation of the sample-space may be cumbersome and can even lead to mistakes. In such cases we may build the sample space by using the probability tree, and use it to find the probability of various events.
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