Decision on Uncertainty
Decision on Uncertainty
Decisions are made every day by individuals. These decisions are made armed with knowledge regarding the outcome of a decision or made with uncertainty of the outcome. Probability is tool of measurement used to determine the likelihood of an occurrence during an event. Because people are often challenged with uncertainty when making a decision the probability concept is important in the decision making process.
Statistics are used for probability analysis of events that cannot be controlled. Many decisions are often made with a significant lack of knowledge and probability helps to determine the unknown. Further, when comparing several alternatives it is often difficult to make a decision regarding which alternative to ...view middle of the document...
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■ Within the sample space, there exists an event B, for which P(B) > 0.
■ The analytical goal is to compute a conditional probability of the form: P( Ak | B ).
■ You know at least one of the two sets of probabilities described below.
• P( Ak ∩ B ) for each Ak
• P( Ak ) and P( B | Ak ) for each Ak
For example, Bob is building a deck tomorrow. The weather person has predicted that it will snow. Historical weather data indicates that it snows only twice each year. When it actually snows the weather person correctly forecasted snow 95% of the time. When it does not snow the weather person incorrectly forecasts snow 5% of the time. The probability of it snowing tomorrow is calculated as follows:
Event A1 = snows tomorrow
Event A2 = it does not snow tomorrow
Event B = the weather person predicts snow
P( A1 ) = 2/365 =0.0054794 [It snows 2 days out of the year.]
P( A2 ) = 363/365 = 0.994520 [It does not snow363 days out of the year.]
P( B | A1 ) = 0.95 [When it snows, the weather person predicts rain 95% of the time.]
P( B | A2 ) = 0.05 [When it does not snow, the weather person predicts rain 5% of the time.]
P( A1 ) P( B | A1 )
P( A1 | B ) = -----------------------------------------------------------
P( A1 ) P( B | A1 ) + P( A2 ) P( B | A2 )
P( A1 | B ) = (0.0054794)(0.95) / [ (0.0054794)(0.95) + (0. 994520)(0.05) ]
P( A1 | B ) = 0.095
The results implicate that even when the weather person predicts snow, it only snows about 9.5% of the time. There is a very good chance that it will not snow tomorrow and Bob can build his deck as planned.
According to Wiggins (n.d.) Bayes's theorem is used in any calculation in which a marginal probability is calculated and such a calculation is so general that almost every application of probability or statistics must invoke Bayes' theorem at some point. Thus, the theorem is helpful when thinking specifically about uncertainty.