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### 11.2 Theoretical and Experimental Probability

9.4.3.2 Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes.

Guiding Question: What is the difference between theoretical and experimental probability?

- Lesson Objective: I will be able to find the theoretical and experimental probability of an event.

- What is the most popular number when rolling 2 dice and adding them?
- Which happens more when flipping a coin, heads or tails?

Guiding Question: What is the difference between theoretical and experimental probability?

- Terms to know
- Probability
- Event
- Outcome
- Sample Space
- Complement
- Theoretical & Experimental Probability
- Geometric Probability
- Experiment

- Probability
- Measure of how likely something will occur.
- Always a fraction/decimal between 0 and 1
- Written as P(event)=
- Probability of 0 means it will never occur (Vikings winning a super bowl)
- Probability of 1 means it will happen (I will sleep tonight).

Guiding Question: What is the difference between theoretical and experimental probability?

- Event – Something that happens
- Outcome – result of event
- Sample space – all possible outcomes

- Example
- Event: draw a card
- Outcome: draw an ace
- Sample Space: Ace – King

Guiding Question: What is the difference between theoretical and experimental probability?

Theoretical Probability –

Complement – all outcomes that are not favorable

Ex. P(flipping heads) = ½

P(not flipping heads) = 1 – ½ = ½

- What is the probability of drawing a king?
- What is the probability of drawing the king of hearts?
- What is the probability of drawing a face card?
- What is the probability of not drawing a face card (complement)?

Guiding Question: What is the difference between theoretical and experimental probability?

Geometric Probability: probability by using the ratio of area or volume.

Ex. If the rectangle is 14 x 12 inches, what is the probability of landing in the triangle?

Guiding Question: What is the difference between theoretical and experimental probability?

Experimental Probability

Theoretical Probability

- Actually performing trials
- Ex. Rolling a die and counting how many times 4 comes up

- Perform no trials
- Ex. You would expect to roll a die and get 4 of the time.

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