Summary
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 possible outcomes.
- Probability of an event — the likelihood of an event occurring. Example: The probability of flipping heads on 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 — the expected probability based on all possible outcomes. Example: The theoretical probability of rolling a 4 on a die is 1/6.
- Experimental probability — the probability based on actual experiments or trials. Example: If a spinner lands on 5 two times out of ten spins, the experimental probability is 0.2.
- Sample space — all the possible outcomes of an experiment. Example: The sample space for a die is {1, 2, 3, 4, 5, 6}.
Exam Tips
Key Definitions to Remember
- Probability of an event
- Mutually exclusive events
- Independent events
- Theoretical probability
- Experimental probability
- Sample space
Common Confusions
- Mixing up theoretical and experimental probability
- Confusing mutually exclusive events with independent events
Typical Exam Questions
- What is the probability of rolling a 4 on a 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 die and flipping a coin independent events? Answer: Yes, because the outcome of one does not affect the other
What Examiners Usually Test
- Understanding and calculating probabilities
- Differentiating between theoretical and experimental probability
- Identifying mutually exclusive and independent events