JAMB Mathematics · Section V
Study notes for Probability: — part of the JAMB UTME Mathematics syllabus. 3 learning objectives with explanations and exam tips.
Permutation means arranging things where order matters, while combination means selecting things where order doesn't matter. Think of it like this: if you're arranging students in a queue for JAMB registration, the first person matters differently from the second person—that's permutation. But if you're just picking three friends to share your lunch, it doesn't matter who you pick first—that's combination.
For example, arranging three WAEC subjects (Math, English, Physics) in order gives 3! = 6 different arrangements. But selecting any two subjects from four available subjects uses the combination formula.
The permutation formula is P(n,r) = n!/(n-r)!, while combination is C(n,r) = n!/[r!(n-r)!]. Notice combination has an extra r! in the denominator—this removes the "order doesn't matter" effect.
Probability measures how likely something is to happen. Think of it as a chance or possibility. When you flip a coin, there are two possible outcomes: heads or tails. Each has a probability of one-half or 0.5, meaning it's equally likely to happen.
The basic formula is: Probability = (Number of favorable outcomes) ÷ (Total number of possible outcomes).
Consider a practical Nigerian example: imagine a bag containing 5 red balls and 3 blue balls. If you pick one ball randomly, the probability of getting a red ball is 5 ÷ 8, which equals 0.625 or 62.5%. This tells you that you're more likely to pick red than blue.
Probability values always fall between 0 and 1. Zero means impossible, while 1 means certain. Most real events fall somewhere in between these extremes.
Think of probability as measuring how likely something is to happen. The addition rule applies when you want the probability of one event OR another happening. For example, if you're picking a student at random from your class to represent JAMB candidates, the chance they studied Mathematics OR Physics is found by adding those separate probabilities. However, you must subtract any overlap to avoid counting twice.
The multiplication rule applies when you need one event AND another to both happen. Imagine selecting two students consecutively without replacement—the probability the first studied Biology AND the second studied Chemistry uses multiplication. Each event depends on the previous one, changing the total possibilities.
These rules form the foundation for solving complex probability problems in JAMB.