Composite Events in Probability

Composite events are applicable for mathematics and statistics to understand the probability of a group of events. For example, a group of coins is tossed and the probability of each head is a calculation for mathematics. A simple event has a single estimated outcome. Simple events include tossing one coin whereas composite events include tossing a group of coins. Therefore, a composite event is a combination of more than one simple event. This article describes the composite events in probability and statistics.      

What is a Composite Event in Probability?

Composite or complex event refers to a combination of simple events. The introduction section has already mentioned the simple and composite event. The composite events in probability require more than one variable (mostly two). For instance, during an occurrence of an event, the possible number of outcome estimations is considered a “simple event”. On the other hand, when the time of occurring an event is considered along with an estimation of outcome, the event is known as a Composite event. Tossing coin has been mentioned in the introduction, which determined both the composite and simple event. If a person determines the time of getting heads and tails, the coins will require estimation. To simplify, not all coins will provide head/tail at the same time. Therefore, the outcome is considered a simple event and the time difference is considered another simple event. Together, those two events can be considered composite/complex events.

The probability is determined by a formula: “Number of times it occurs”/total number of possible outcomes”. In the case of Composite events, the two simple events are occurring independently. Usually, the probability for a composite event is calculated by multiplying the “probability of the first event” with the “probability of the second event”. Another simple example of composite probability is “flipping a coin twice”. This example is highly similar to the example mentioned in the introduction. It demonstrates that the chance of “getting head” in a single event is 0.50 and the chance is 0.50 when the coin is tossed for a second time. Therefore, the composite/compound probability is 0.50×0.50=0.25. Alternatively, the composite probability is 25 %. The composite event can also be regarded as the compound event or complex event as probability is estimated for more than one simple event.

Importance of Composite events in probability 

The composite event in probability is mostly used by “insurance underwriters” for assessing the risks and opportunities in the market of insurance. For instance, the “underwriters” calculate the probability of a married couple reaching a particular age. The composite probability is measured by understanding the simple probability of a single member of the couple.

Another use of composite probability is observed in detecting the odds of two individual climate changes in a single region. For example, the underwriters use a composite probability method to determine the probability of occurring two individual hurricanes at the “same time”. The calculation is if two “mutually exclusive” (ME) events are observed, then, the probability is calculated by the addition of the two probabilities. Contrarily, “Mutually Inclusive” (MI) events are those that cannot occur when another event is occurring.

Probability formulas for calculating composite events

As previously mentioned, there are two types of composite events; one is ME and another one is MI. In this context, ME can occur in the presence of others whereas MI cannot occur in the presence of others.

For example, X and Y are two events. 

Formula for ME in probability: “P (X or Y) = P (X) + P (Y)” [P = Probability].

Formula for MI in probability: “P (X or Y) = P (X) + P (Y) – P (X and Y)”.

Another way to demonstrate the composite probability is using the “Area Model”. For example, if someone flips a coin and expects a tail; and rolls a die and expects even numbers, the calculation is “3/12 [Rolling die (Total 6 numbers) x Head of Tail (2 event) = 12 events] = ¼ or 25%”.

Conclusion

The article has explained the composite events in probability. During the explanation, it was essential to mention simple events as well. Therefore, the simple probability calculation has been explained and it was compared with the composite probability. The study found that the calculation of composite probability has importance in determining the chance of hurricane occurrence or determining the risk in insurance companies. After that, the article clearly demonstrates the formula for calculating the probability for composite events. A formula for simple events has been provided as well for a comparison. Lastly, the study upheld some FAQs.