The AND / OR Rules (Edexcel GCSE Maths): Revision Notes
The AND/OR rules
Introduction to combined probability
When dealing with probability problems involving multiple events, you need to understand how to combine the probabilities of different outcomes. This topic focuses on situations where you have two or more events happening, and you need to calculate the probability of different combinations of these events occurring.
The key to success with these problems is understanding when to use the AND rule versus the OR rule, and knowing how to apply the correct formula for each situation.
Combined probability problems are fundamental in statistics and appear frequently in exams. The main challenge is determining which rule to apply in different scenarios.
General approach to solving probability problems
When you encounter a complex probability question involving multiple events, follow this systematic approach:
The most important strategy is to break down complicated probability questions into a sequence of separate single events. This means:
- Identify each individual event that could occur
- Calculate the probability of each separate event happening
- Then apply the appropriate AND or OR rule to combine these probabilities
Step-by-Step Problem Solving
This systematic method prevents confusion and ensures you don't miss any important details in the problem. Always tackle complex probability questions by working through individual events first.
The AND rule
The AND rule helps you find the probability that both events will happen. When you want to calculate the probability of event A AND event B both occurring, you multiply their individual probabilities together.
Formula:
This rule works when the two events are independent, meaning the result of one event doesn't affect the outcome of the other event.
Let's look at how this works in practice:
Worked Example: Dave's Ball Selection
In this example, Dave is picking balls from two different bags. To find the probability that he picks a yellow ball from both bags, you need to:
- Find the probability of picking yellow from bag X
- Find the probability of picking yellow from bag Y
- Multiply these probabilities together
The calculation shows that picking yellow from bag X has a probability of , and picking yellow from bag Y has a probability of .
Using the AND rule:
The OR rule
The OR rule helps you find the probability that at least one event will happen. When you want to calculate the probability of event A OR event B occurring (or both), you add their individual probabilities together.
Formula:
This rule works when the two events are mutually exclusive, meaning they cannot both happen at the same time.
| Colour | red | blue | yellow | green |
|---|---|---|---|---|
| Probablity | 0.25 | 0.3 | 0.35 | 0.1 |
Worked Example: Probability Spinner
This example shows a probability spinner with different coloured sections. To find the probability of spinning either red or green, you add the individual probabilities:
The probability of landing on red is , and the probability of landing on green is .
Using the OR rule:
Common mistakes and memory aids
One of the most frequent errors students make is confusing when to use addition versus multiplication. Here's a helpful way to remember:
- AND means multiply - when both events must happen
- OR means add - when at least one event must happen
Critical Memory Warning
The textbook provides this important warning: "The way to remember this is that it's the wrong way round — you'd want AND to go with '+' but it doesn't. It's 'AND with ×' and 'OR with +'. Once you've got your head round that, try this exam practice question."
This counter-intuitive nature is exactly why many students struggle with these rules initially. Practice with the correct associations until they become automatic.
Remember!
Key Points to Remember:
- Always break complex probability problems into separate single events first
- The AND rule uses multiplication:
- The OR rule uses addition:
- AND rule applies when both events must happen (independent events)
- OR rule applies when at least one event happens (mutually exclusive events)