Study Notes
Probability is the measure of how likely an event is to occur, expressed as a number between 0 and 1. It can be calculated using theoretical or experimental methods.
- Probability — the likelihood of an event happening. Example: The probability of getting heads when tossing a coin is 1/2.
- Mutually Exclusive Events — two 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.
- Theoretical Probability — calculated based on known possible outcomes. Example: The probability of rolling a 4 on a fair die is 1/6.
- Experimental Probability — calculated based on actual results from 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 and independent events
Typical Exam Questions
- What is the probability of rolling a 3 on a fair die? Answer: 1/6
- If a coin is tossed 100 times and lands on heads 60 times, what is the experimental probability of getting heads? Answer: 0.6
- Are rolling a die and flipping a coin independent events? Answer: Yes, they do not affect each other.
What Examiners Usually Test
- Understanding and calculating probabilities
- Differentiating between theoretical and experimental probability
- Identifying mutually exclusive and independent events