Relative Frequency Probability

Relative Frequency

We often use relative frequency to determine probabilities for a particular population. The relative frequency probability is the number of events in the population that meet the condition divided by the total number in the population.

Relative Frequency Probability
The relative frequency probability is the limit of the proportion of times that event A occurs in a large number of trials, n:
                    P(A) = 

where nA is the number of A outcomes and n is the total number of trials  or outcomes. The probability is the limit as n becomes large (or approaches infinity).

Example: Probability of Incomes Above $50,000.
Sally Olson is considering an opportunity to establish a new car dealership inDakota Country, which has a population of 15,000 people. Experience from many other dealerships indicates that in similar areas a dealership will be successful if at least 40% of the households have annual incomes over $50,000. She has asked Paul Smith, a marketing consultant, to establish the proportion of family incomes above $50,000, or the probability of such incomes.

Solution: After considering the problem, Paul decides that the probability should be based on the relative frequency. He first examines the most recent census data and finds that there were 54,345 households in Dakota Country and that 31,496 had incomes above $50,000. Paul computed the probability of event A from this source as                

Since Paul knows that there are various errors in census data, he also consulted similar data published by Sales management magazine. From this source he found 55,100 households, with 32,047 having incomes above $50,000. Paul computed the probability of event A from this source as

Since these numbers are close, he could report either. Paul chose to report the probability as 0.58.