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Probability: Single Events
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What you will learn from this videoWhat you will learn
- We'll learn about the probability of an event happening.
- We will also learn how to PREDICT the chances of an event happening.
- And we'll see how this knowledge can help us compete in sports, be on a game show, and understand bottle tricks!
- Discussion Questions
Before Video
What is a frequency?ANSWERA frequency is a measure of how often something happens. It is often a count of successes for a given number of trials.
Answers will vary.
If an event is likely, then we are pretty sure it will happen, but it may not.
If an event is unlikely, it means it probably won’t happen, but it could.
Some examples are rolling number cubes, flipping coins, shooting baskets, winning a game, and winning the lottery.
After Video
What is a probability?ANSWERProbability is the extent to which something is likely to occur. Probabilities have values between 0 and 1, describing likelihoods from impossible (0) to certain (1).
A probability model describes how probability is distributed amongst all possible outcomes in a sample space. In a uniform probability model, all outcomes are equally likely. In a non-uniform probability model, some outcomes are more likely than others.
A theoretical probability is one you calculate based on the number of outcomes possible and the number of outcomes in the event.
An experimental probability is one you calculate by conducting an experiment and determining the frequency of an event in a fixed number of trials.
Likelihood increases with larger numbers. Since 0.6 is larger than 0.2, it is more likely to snow than to rain.
- Vocabulary
- Probability DEFINE
The extent to which an event is likely to occur. Probability is expressed using numbers between 0 and 1.
- Impossible DEFINE
An event that cannot happen is impossible. Events that are impossible have a probability of 0.
- Likely DEFINE
An event is likely if we are pretty sure it will happen, but it still may not happen. Likely events have probabilities close to 1.
- Unlikely DEFINE
An event is unlikely if we are pretty sure it won’t happen, but it still may happen. Unlikely events have probabilities close to 0.
- Certain DEFINE
An event that will happen for sure is certain. Events that are certain have a probability of 1.
- Equally likely DEFINE
If two events have the same probability, then the events are equally likely. If two outcomes have the same probability, then the outcomes are equally likely.
- Event DEFINE
A set of possible outcomes that result from a particular experiment or situation. For example, when rolling a number cube to move a playing piece, the event “roll 4 or higher” includes the set of outcomes {4, 5, 6}.
- Trial DEFINE
The result of an experiment. For example, when determining the experimental probability of getting heads on a coin flip, each coin flip is a trial.
- Outcome DEFINE
Any potential result in an experiment. For example, when flipping a coin there are two outcomes: {heads, tails}; when rolling a number cube there are 6 outcomes: {1, 2, 3, 4, 5, 6}.
- Frequency DEFINE
The number of times an event happens during an experiment is the frequency of the event.
- Expectation DEFINE
The product of the theoretical probability and the number of trials in the experiment gives the expectation, or expected frequency, for an event in that experiment.
- Experimental probability DEFINE
A probability determined by experimental trials.
- Theoretical probability DEFINE
A probability that is calculated. For events with equally likely outcomes, the theoretical probability is the number of ways the event can happen divided by the total number of outcomes in the sample space.
- Sample space DEFINE
The set of all possible outcomes in an experiment.
- Law of Large Numbers DEFINE
As the number of trials in an experiment increases, the experimental probability gets closer to the theoretical probability. So, if you want to determine the probability of an event using an experiment, you need a lot of trials to get an accurate value of the experimental probability.
- Probability DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide