What is Compound Probability?
Mathematicians, scientists, various national Governments and various industries have been applying the concept of probability since times immemorial.
From assessing the likelihood of occurrence of rainfall in weather forecast to calculating the likelihood of a cricketer scoring a six in a match, from calculating the possibility of a leader getting elected in the next elections to the possibility of a rise in the demand for sanitisers, we live in a world that practically revolves around the concept of probability.
Who knew that a simple process of ‘guesswork’ would change the way we look at the world?
Here are a few pointers to help you understand the concept of probability and compound probability.
Meaning of probability
Probability is the measure of the likelihood or the possibility of the occurrence of an event. There are many events that occur without any certainty, and the availability of relevant data that can predict the possibility, makes the process of decision making easier.
For example: Imagine that there is a deck of cards in question, the chance of pulling out an ace is 4 in 52 (since there are 4 aces in every deck of 52 cards), making 1/13 the probability of pulling out an ace.
Further, if the event in question was pulling out an ace of diamonds, then the probability would be 1/52 (since there is only 1 ace of diamonds in a deck of 52 cards).
Further, if the event in question was to pull out a red ace, then the probability would be 2/52, which is 1/26 (since there are 2 red aces in a deck of 52 cards).
Meaning of compound probability
More often than not, you will come across a situation where knowing the probability of just one event would not suffice. Sometimes, there could be two or more events that need assessment to be able to provide credible and reliable data for use. In a case like this, two independent events are taken and assessed. The product of the individual probabilities of both events is known as the compound probability of the said two events.
In other words, the product of the probability of one event and the probability of another event is termed as a compound probability.
History of compound probability
Ever since the 16th century, a grading system was developed, in which, by the law of evidence, credibility and available proof would predict the verdict of a court of different cases. This attracted the attention of many famous experts like Pascal, Fermat, and Cordano.
With every century, every decade, and every day, the history of probability got richer.
Fisher’s work on hypothesis testing made probability a very integral part of the world of mathematics and statistics, and by the twentieth century, the concept of compound probability gained popularity.
Usage of compound probability in daily life
It may come to you as a surprise, but we use the applied concepts of probability almost on a day-to-day basis.
Remember how every time your friend has said that they will be on time, you have estimated a 90% chance that they will be at least an hour late?
The very assessment of the likelihood of a friend coming to meet you on time is the entire basis of the principle of probability.
Let us imagine two independent events – Your friend’s late arrival and a movie starting later than scheduled.
Finding the answer to the question, “what is the possibility of your friend arriving earlier and the movie starting later than scheduled?”
The multiplication of both the probabilities will be a compound probability!
Basic observations of compound probability
- The answer to every question of probability is always between zero and one.
- The sum of the probabilities of all the possible outcomes will always add up to one.
- The concept of zero probability exists since there are many events which have zero chance of occurring — for example, the possibility of getting both head and tail in a single toss of a coin.
- In a finite space of samples, if zero probability is a probability then so is the probability of attaining 1. The probability of attaining either heads or tails in a coin toss is 100%, and hence, its probability would be 1.
Application of compound probability
Let us imagine that you are a huge fan of IPL. You end up challenging your friend that Virat Kohli will hit more sixes than M S Dhoni and at the same time, you will get your amazon order before the next match.
Both events are independent of each other and do not influence each other in any way.
Assuming upon analysis
- Observations have proved that M S Dhoni has hit 36 sixers in 5 matches while Virat Kohli has hit 20 sixers in 7 matches. Clearly, the chances of Virat Kohli hitting more sixers than M S Dhoni are thin.
- Observations have also proved that your amazon order has always arrived before the date of delivery and seeing that the match is a day after your scheduled date of delivery, there is a very high chance that you will receive your order in time.
- The product of both these probabilities will be the compound probability of these two independent events. This data will further give you an estimate and aid you in the process of decision-making.
Advantages of compound probability
- Compound probability has proven to be a very effective and reliable method of calculating possible outcomes of various individual events together.
- The application of compound probability widens the scope of the field of probability and helps facilitate data for further use.
- Compound probability is a concept that brings together the best of both worlds by not only providing information but also increasing the authenticity of the results.
Disadvantages of compound probability
- While the concept of compound probability has proven to be highly effective since centuries, many would argue that the compound probability and its calculations are still not facilitating sure-shot data.
- The fact that the calculation of probability does not help in changing the results is another argument that might render the application of compound probability redundant.
FAQs on compound probability
- What is a compound event probability?
A compound event is the occurrence or happening of an event with the probability of more than one outcome. In cases like these, the compound event probability is calculated very carefully, and any overlapping probabilities are removed out of the equation.
The compound event probability is a highly reliable calculation and is known to yield authentic results.
- Why do we multiply various probabilities?
The very idea of multiplication signifies “expansion”. Expanding and exploring the various probabilities of the occurrence of events and to assess their products is the foundation of the very concept of probability.
Various probabilities are multiplied to widen the scope of the results while ensuring their correctness and reliability.
- What is the difference between simple and compound probabilities?
Assessing the probability of the occurrence of a single independent event is known as simple probability.
Compound probability, on the other hand, is a concept that calculates the probability of the occurrence of two or more individual and independent events.
Independence of events means that the outcome of one event does not affect the outcome of the other.
- What is an event in compound probability?
An event is the happening or the outcome of an experiment.
A defined collection of outcomes is known as the event of that experiment, and an “event” is the basic foundation and focus around which all the calculations are done. A compound probability is calculated by multiplying the probabilities of two or more individual events.
- What is “or” in probability?
The words “and” and “or” hold huge significance in the study of probability. The word “or” signifies various possible outcomes of an experiment, whereas the word “and” could signify compound probability.
For example, a simple coin toss could lead to heads or tails. A coin tossed twice in a row could lead to various compound probabilities like “heads and tails”, “heads and heads”, “tails and tails” or “tails and heads”.
Compound probability is a study that has facilitated highly reliable data and has helped in the growth of various fields of mathematics and science.
To excel in the field of probability and nail the outcomes, one must and should know the types of data with examples with regards to the applications and usage of this concept.
There are various formulae related to probability and various examples that could help you understand the concept much better and further increase your probability of scoring better in your next test.