Study Notes
Probability is the maths of chance, expressed as a number between 0 and 1, indicating how likely an event is to occur. Probabilities can be written as fractions, decimals, or percentages. An event is the set of possible outcomes of an experiment, such as tossing a coin, which has two possible outcomes: Head or Tail. Equiprobable — outcomes that have an equal chance of occurring. Example: Tossing a fair coin results in heads or tails, both with equal probability.
- Exhaustive events — all possible outcomes of an experiment. Example: In a coin toss, heads and tails are exhaustive events.
- Mutually exclusive events — events that cannot happen at the same time. Example: Rolling a die and getting a 3 or a 4 are mutually exclusive events.
- Independent events — the occurrence of one event does not affect the other. Example: Flipping a coin and rolling a die are independent events.
- Conditional probability — the probability of an event occurring given that another event has already occurred. Example: The probability of drawing an ace from a deck, given that a king has already been drawn.
Exam Tips
Key Definitions to Remember
- Probability is a measure of how likely an event is to occur.
- Mutually exclusive events cannot happen at the same time.
- Independent events do not affect each other's outcomes.
- Conditional probability is the probability of an event given another event has occurred.
Common Confusions
- Confusing mutually exclusive events with independent events.
- Misunderstanding the difference between probability and odds.
Typical Exam Questions
- What is the probability of drawing a red card from a deck of cards? Answer: 1/2
- If two dice are rolled, what is the probability of getting a sum of 7? Answer: 6/36 or 1/6
- What is the probability of flipping a coin and getting heads twice in a row? Answer: 1/4
What Examiners Usually Test
- Understanding and applying probability rules and formulas.
- Ability to use Venn diagrams and tree diagrams to solve probability problems.
- Calculating probabilities of combined events using addition and multiplication rules.