# Simple Probability

Last updated: September 30, 2021

## What Does Simple Probability Mean?

Simple probability is the calculation of an outcome or the chance of an event ever happening. Insurance companies use probability statistics to determine the chances of having to pay out a claim.

A simple probability is calculated by dividing a specific outcome by all the possible outcomes. For instance, when flipping a coin, there are two outcomes: heads or tails. To find the probability of getting either heads or tails, divide one outcome (1) by the two possible outcomes (2). Dividing 1 by 2 results in .50 or 50%.

Insurance companies must take into account many more than two outcomes, as life is not as simple as a 50/50 coin toss. However, they use the same basic formula to determine how much they are likely to pay out to sets of policyholders who have the same type of policy. This result gives them an idea of how much money they need to collect to cover their potential losses (the amount they pay out).

Going back to the coin example, on the first two flips, the 50/50 split that one would expect with a 50% probability may not occur — it may land on heads twice, then tails, then heads again. This makes the probability of getting one outcome less predictable. This is where the law of large numbers comes in. The law of large numbers states that the more data points there are, the more accurate an outcome prediction will be. Continuing to flip the coin and record the results (say, 100 times or more), the probability will become closer to 50%.

## Insuranceopedia Explains Simple Probability

Insurance companies hire actuaries, highly trained professionals in probability statistics and data analysis, to determine the likelihood of an event happening. Actuaries study and train for at least 6–10 years to more accurately predict outcomes.

Based on the probability of the event, the insurance company will determine the likelihood of having to pay out on a certain type of claim (outcome). Looking at these results, the company determines how much money they will need to gather in order to pay out the claims that are made for that year. They will collect this money through insurance premiums.

If it is not likely to happen, the insurance premium for one coverage will be less expensive than a claim for something that is more likely. For example, if a town historically gets a lot of hail, the premium for that coverage will likely be high. If that same town is far from large bodies of water and waterways, flood coverage will likely be cheap.

Another concept actuaries use is weighted probability. Because there are usually more than one or two factors (not simply heads or tails) when it comes to predicting life events, actuaries have to factor in not only the possible outcomes, but the desired outcomes and how many ways one can get to those outcomes.

For example, rolling one die, the probability of rolling a two would be the same as rolling a four: 1/6. But by rolling two dice, there would be a greater chance of rolling a score of four than of two. This is because there is only one combination to get two when using two dice (1, 1), but four can be scored with more than one combination (1, 3 or 2, 2 or 3, 1). This means the probability of scoring four is weighted heavier than two.

To determine weighted probability, determine the total number of possible outcomes (total values) in the scenario. Then, determine how many ways the outcome can occur. Divide the number of ways to achieve the outcome by the number of possible outcomes.

Going back to the example of the two dice, when trying to determine the weighted probability (%) of rolling a score of four with two dice, the total number of possible outcomes is 36 (6 sides × 6 sides = 36 outcomes). There are three ways to achieve this roll (1, 3 or 2, 2 or 3, 1). The final calculation is as follows:

3 preferred outcomes ÷ 36 possible outcomes = 0.083 or 8.3%

Again, the insurance companies factor in a huge number of outcomes and ways to achieve those outcomes when deciding what is or is not covered, which is why they rely on highly trained professionals to crunch the big numbers. The bottom line is that insurance companies do not just randomly decide what is and is not covered. They do the math to make sure they can sustain their financial health so they can protect their clients. 