For this discussion, I choose an insurance scenario. It is among the real-life scenarios where one has to weigh several factors and decide the best plan and deductibles. For instance, when choosing a car insurance policy, I may consider the following concerns.

1. How likely will I file a claim?
2. How much would the accident cost?
3. How much am I willing to pay in deductibles?

In these scenarios, I may find the answers by considering the number of accidents per 100 drivers, their causes, and the costs of repairs. For instance, in every 100 drivers, 12 have involved in an accident per year, where eight were deer hits.  Average repairs cost $3000.

In such a scenario, the best car insurance plan may be found by considering probability elements. A probability space models random variables in this way: (a) Sample space is a set of all outcomes. For example, for every trip, which desired and undesired outcomes are likely to arise. (b) Event space, which is a set of all events. For instance, which events might lead me into requiring a car insurance cover? (c) probability function, which is the percentage chance of an event to happen. For instance, a 12 % chance to involve in an accident, and 8% to hit a deer in my case. Therefore, I may consider a random variable with the element’s event and cost. That is, If I am a slow driver, my chances of hitting a deer may reduce further, and if I hit one, only minor repairs would be needed. That is a typical conditional distribution which considers that if an event A and B in F happens, and the outcome of B is known, then it would influence the probability space of A (Kuan, 2004). Since I am fairly a fast driver, I may need to insure my car on a comprehensive plan – not just liability, with deductibles more than the average $3000 incurred by other drivers.

References

Kuan, C.-M. (2004). Chapter 5: Elements of Probability Theory. http://homepage.ntu.edu.tw/~ckuan/pdf/et01/et_Ch5.pdf.