Study Notes
Probability is the measure of how likely an event is to occur. It is calculated by dividing the number of ways an event can happen by the total number of outcomes.
- Probability — a measure of the likelihood of an event occurring Example: The probability of flipping heads on a coin is 1/2.
- Mutually Exclusive Events — events that cannot happen at the same time Example: Rolling a 2 or a 3 on a die.
- Independent Events — events where the outcome of one does not affect the other Example: Tossing a coin and rolling a die simultaneously.
- Theoretical Probability — likelihood of an event based on all possible outcomes Example: The probability of rolling a 4 on a fair die is 1/6.
- Experimental Probability — likelihood of an event based on actual experiments Example: If a spinner lands on 5 two times out of ten spins, the experimental probability is 0.2.
- Sample Space — all possible outcomes of an experiment Example: The sample space for a die roll is {1, 2, 3, 4, 5, 6}.
Exam Tips
Key Definitions to Remember
- Probability
- Mutually Exclusive Events
- Independent Events
- Theoretical Probability
- Experimental Probability
- Sample Space
Common Confusions
- Confusing theoretical probability with experimental probability
- Misunderstanding mutually exclusive events as independent events
Typical Exam Questions
- What is the probability of rolling a 3 on a fair die? Answer: 1/6
- If a coin is flipped 100 times and lands on heads 60 times, what is the experimental probability of heads? Answer: 0.6
- Are rolling a 2 on a die and flipping a head on a coin mutually exclusive? Answer: No, they are independent events.
What Examiners Usually Test
- Understanding and calculating probabilities
- Differentiating between theoretical and experimental probability
- Identifying mutually exclusive and independent events