Probability is a very important topic that sets the stage for jobs in the field of consultancies, data analysis and data sciences. More advanced probability problems keep emerging even nowadays, a proof of why the topic is a very fresh one and this is a reason why it can be integrated with large scale complex topics of Artificial Intelligence, Big Data Analytics and Machine Learning. Let us explore some basic tips and tricks that will help set the tone for your higher secondary probability.
- Know the difference between AND/OR
Reading the problems and following each step described in the question would be a very essential skill and a step for working out probability problems faster and faster. Know what the problem tries to tell us. AND that connects events in the question indicates multiplication in your problem when you work out mathematically and OR indicates addition should be used while connecting two events.
- Know the difference between Mutually exclusive and Independent events
If you say two events are mutually exclusive it is not the same as saying the two events are independent. Mutually exclusive events are those that cannot happen at the same time and Independent events don’t depend on each other. Thus they do not mean the same thing.
Independent Events A and B, P(A and B) occurring is P(A) * P(B) whereas Mutually Exclusive Events A and B indicates that P(A and B) occurs with 0 (zero) probability.
- Independent Random Variables in your problem
If two variables (events) in your problem are said to be independent they have zero correlation between each other. This is a converse stress on Point 2.
If two events A and B are independent, then
P(A|B) = P(A) i.e. probability of A occurring when probability of B occurring is excluded is the same. Thus P(A ∩ B) = P(A) * P(B) (Intersection of two events A and B).
- Visualize the problem
Try to apply the logic to your problem visually by extending it to Venn Diagrams and Sets if it becomes more difficult to understand just in your mind. If the problem states more than 3 to 4 events it sometimes helps visualize the problem with Venn Diagrams.
- Apply Bayes Theorem at the following conditions
When the sample space consists of n mutually exclusive events A1, A2, … , An and within the sample space there exists an event X for which P(X) > 0, only then apply Bayes Theorem.
- Conditional Probability
This type of problem is special since it restricts the playing field for us by stating that some part of the problem had already happened. The general equation of probability becomes:
P(A|B) = P(A ∩ B) /P(B). This is the probability of A occurring when B has already occurred.
- Sometimes write all the possible cases
Formulae don’t give us the results all the time in this topic. Hence for problems like Cards, Coins, Dices it is better to write the possible cases and determine individual probabilities of each of the cases then OR them/AND them according to the problem demand. This will give a perfect solution if done completely and will never fail you.
Probability is not necessarily a difficult topic to master but it is definitely not easy as well. Solve more and more questions to get a hang of the type of phrasing question setters use and once you do that, you will be able to ace the topic.
Permutations and Combinations is another topic that goes hand-in-hand with probability. Read here about how to master this topic!