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#### Presentation Transcript

**1. **Probability Part I

**2. **Probability Probability refers to the chances of an event happening.
Symbolize P(A) to refer to event A.

**3. **Values of Probability All values are between 0 and 1.
Write answers as 3 place decimals.
If P(A) = 0, it means the event WILL NOT happen.
If P(A) = 1, it means the event WILL happen.

**4. **Relative frequency approximation of probability
Conduct an experiment a large number of times.

**5. **Example Toss a coin 10 times, recording whether you saw a head or a tail.
P(Head) =
Class results
P(Head) =

**6. **Theoretical probability Based upon what should occur, if events are equally likely.

**7. **Example If you toss a single coin, what is the probability of getting a head?

**8. **Example A die is rolled.
What is the probability that the number showing is greater than 2?
What is the probability that the number showing is at least 2?

**9. **Die roll continued What is the probability that the number showing is less than 2?
What is the probability that the number showing is at most 2?

**10. **Example A card is selected from a standard deck of cards.
What is the probability that it is a King?
What is the probability that it is a red card?
What is the probability that is a club?

**11. **Law of Large numbers
If an experiment is repeated again and again, the relative frequency probability of an event tends to approach the theoretical probability.

**12. **Complement of an event Symbolized:
Represents the chances an event will not happen
Found by:

**13. **Example What is the probability for each, using complements:
The card is not a king
The card is not red
The card is not a club

**14. **Tree Diagram
Used to show all of the possible outcomes of an experiment

**15. **Example
A couple plans on having 3 children. Assuming that the births are single births, make a tree diagram.

**16. **Questions Find each probability:
All 3 children are girls
There is one girl
There is at least one girl
There is at most one girl

**17. **Addition Rule for 2 events P(A or B) means P(event A happens OR event B happens OR they both happen)
P(A or B) = P(A) + P(B) – P(A and B)

**18. **Example
A card is drawn from a deck of 52 cards. What is the probability that it is either a King or a Heart?

**19. **Example
A card is drawn from a deck of 52 cards. What is the probability it is a King or a Queen?

**20. **Mutually Exclusive Two events are mutually exclusive if they can not both occur at the same time.
P(A and B) = 0
P(King and Queen) =

**21. **Tables to present data To test the effectiveness of a new drug, trials are conducted where some people get a placebo and others get the drug.

**22. **Questions: If a patient is randomly selected, what is the probability that:
The patient took the drug
The patient found treatment effective
The patient took the drug and it was effective
The patient took the drug or it was effective