Simple Probability

What Does Simple Probability Mean?

Simple probability refers to calculating the likelihood or chance of a specific event occurring. Insurance companies rely on probability statistics to assess the chances of paying out a claim.

To calculate simple probability, divide the number of favorable outcomes by the total number of possible outcomes. For example, when flipping a coin, there are two possible outcomes: heads or tails. The probability of getting either heads or tails is calculated by dividing one favorable outcome (1) by the total number of outcomes (2). This gives a probability of 0.50 or 50%.

For insurance companies, the calculation is far more complex than a simple 50/50 coin toss, as real-life scenarios involve many more possible outcomes. However, the same fundamental formula is applied to estimate the likelihood of paying claims for specific groups of policyholders. This helps insurers determine how much they need to collect in premiums to cover potential payouts.

Returning to the coin example, the expected 50/50 split may not appear immediately within the first few flips. For instance, the coin might land on heads twice, then tails, and then heads again, making the probability of a specific outcome seem less predictable initially. This is where the law of large numbers comes into play. According to this principle, as the number of trials (e.g., coin flips) increases, the observed probability becomes closer to the expected probability. Flipping the coin repeatedly, say 100 times or more, will yield results closer to the theoretical 50%.

Insuranceopedia Explains Simple Probability

Insurance companies employ actuaries, highly trained professionals in probability statistics and data analysis, to assess the likelihood of events occurring. Actuaries typically undergo 6 to 10 years of study and training to improve their ability to predict outcomes accurately.

Based on the probability of an event, the insurance company determines the likelihood of having to pay out a claim for a specific type of coverage. Using these predictions, the company calculates how much money it needs to collect in premiums to cover the expected claims for the year.

If an event is unlikely, the insurance premium for that coverage will be lower than for more probable events. For instance, in a town that frequently experiences hailstorms, hail coverage will likely have a higher premium. Conversely, if the same town is distant from large bodies of water and waterways, flood coverage will likely be cheaper.

Actuaries also use the concept of weighted probability. Life events often involve multiple factors, not just simple outcomes like heads or tails. Therefore, actuaries must consider not only the possible outcomes but also the likelihood of each outcome and the number of ways each can occur.

For example, when rolling one die, the probability of rolling a two is the same as rolling a four: 1/6. However, when rolling two dice, the probability of rolling a total of four is higher than rolling a two. This is because there is only one combination (1, 1) to get a two, but multiple combinations (1, 3; 2, 2; 3, 1) to get a four. Thus, the probability of rolling a four is weighted more heavily than the probability of rolling a two.

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

For the two-dice example, the total number of possible outcomes is 36 (6 sides × 6 sides = 36 outcomes). There are three ways to achieve a total of four (1, 3; 2, 2; 3, 1). The final calculation is:

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

Insurance companies take into account a vast number of possible outcomes and the ways they can occur when deciding what is covered. This is why they rely on actuaries, who use complex calculations to ensure the company remains financially healthy while providing protection for their clients. The bottom line is that insurance companies don’t randomly decide what to cover; they rely on data-driven analysis to maintain stability.