Question

Students will select and discuss one of the following probability rules:

Addition rule

Multiplication rule,

Subtraction, and

Independent rule.

In 6-sentences or more, explain how the rule applies at the workplace or personal life experience.

Answer 1

We should consider the Independence Rule

Two events A and B are said to be independent if your intial beliefs about B are not going to change if you are told that A occured. Intutively the fact that A occured does not convey any information to you about the likelihood of event B. The information provided by A is not relevant to guess whether B is going to occur or not.

Mathematically two events are independent iff their probability of happening simultaneously is equal to the product of their individual probabilities.

P(A B ) = P(A) * P(B)

Now this was some context to the question.

In workplace, for example you are an actuary and you know that there is going to be a decrease in interest rates (which are used to calculate the pension plan liabilities) with some probability .

Also you know the government is planning to pass a new law that is going to increase the pension liabilities for the employers. This also has some probability of occuring.

Now these two events are independent. If the government passes some legislation that increase the pension cost, that would have no impact on the market interst rates that are going to be used to calculate the pension plan's liabilities. Knowing the government has passed the law, does not change our beliefs whether the market interest rates are going to fall (that are used to calculate the pension plan liabilities). This is because they are unrelated with the new legislation passed and are only dependent on the current economic scenario of the market economy.