Revision Tips For Mastering Probability in Secondary Math

Probability is a mathematical way to describe the likelihood of something happening. For example, when we say that someone has a 1 in 10 chance of contracting an illness, or when there is a 30% chance of rain in the evening, we are using probability.

In your math class or secondary math tuition class, students will learn the fundamental techniques of dealing with probability. Most students find that probability is not difficult to grasp, but there are some tricky areas that can seem counterintuitive and abstract.

So, we are going to share some tips on how you can ace your upcoming quiz on Probability!

1. Probability is a percentage

Probability is a percentage, where 1 (100% chance) means the event will definitely happen, and 0 (0% chance) means the event will definitely not happen. So, a quick and easy way to check your answer is to see if your probability is between 0 to 1. If it falls outside of this range, you know it’s time to revisit your workings!

2. Use diagrams to help

The most common type of diagrams in calculating probability are the Possibility diagram, Venn diagram and Probability Tree. The Venn diagram helps you see overlapping events, while the tree diagram shows the sequence and probability of different scenarios happening. Use these to help you list out different probabilities more quickly.

• Possibility diagram

• Venn diagram

• Probability tree

3. Know the three types of events

Beyond the basic concepts of probability, you might be tested on various types of probabilities (depending on where you are in your studies). They could be mutually exclusive, independent, or conditional. Learn how to identify them (it is a good idea to remember one example scenario) and get familiar with the formulae for each of them so that you can apply the right one quickly during your test.

• Mutually exclusive events

Mutually exclusive events are events that cannot occur at the same time. Think: head and tails on a coin; odd and even numbers on a dice; different suits in a deck of playing cards.

Technique: addition

• Independent events

Independent events are events that are not affected by each other. Think: each time you roll a die, the probability of a getting a number is not affected by the previous number you rolled.

Technique: multiplication

• Conditional probability

Unlike independent events, conditional probability is when the probability of one event is affected by another event happening. Think: the probability of drawing a blue ball after a drawing red ball from a bag (the ball is not replaced once drawn).

Technique: tree diagram

4. Present your workings correctly

The actual calculation is usually not too difficult, but it is the workings and presentation that often causes students to lose marks.

Practice enough questions to ensure that writing set notation and probabilities come naturally to you. Develop a good habit of labelling your steps clearly so that the examiner understands what you are trying to do.

5. Checking your answer

Make sure your answer is expressed in a fraction, decimal, or percentage. Check if the question requires you to express your answer in a specific format!

For fractions, make sure your answer is in the most simplified form. For decimal and percentages, check that you have the appropriate number of significant figures (usually 3 s.f.).

Conclusion

The Probability chapter is quite a short one but it can be quite tricky and tedious especially for long questions that involve a string of events. Being careful, detailed, and organised is especially important to excel in this topic!

If you have a Probability quiz coming up, we wish you all the best and we hope this little revision guide can help you gain clarity on this topic! For more math help, we warmly invite you to join us at IP Math Tuition where we revise and discuss math topics weekly in small groups, led by an experienced tutor.

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