1. Warm Up Which of the following are combinations?
4 books pulled at random from a shelf
12 books arranged on a shelf
3 flavors of juice selected from a variety pack

2. Answer Which of the following are combinations?
4 books pulled at random from a shelf
12 books arranged on a shelf
3 flavors of juice selected from a variety pack

3. Basic probability

4. Probability

5. Some Terms! Theoretical probability - what should happen
Experimental probability - what actually happens in real life
Outcome - the result of an experiment
Sample Space - all the possible outcomes of an experiment
Trial - one iteration of an experiment
Event - a specific outcome

6. Experiment: Rolling a die Outcomes: 1, 2, 3, 4, 5, and 6 Sample space: S = {1, 2, 3, 4, 5, 6}

7. Example 1
Consider this dartboard. Assume that the experiment is throwing a dart once and that the dart always hits the board. Find: a) The outcomes b) The sample space

8. Example 2
If an experiment consists of tossing a coin three times and recording the results in order, find the sample space. (Find all possible outcomes). S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

9. Example 2 Continued E = {HHT, HTH, THH}
The event E, showing exactly two heads, consists of all outcomes with two heads. Write the sample space of E.
E = {HHT, HTH, THH}

10. Example 2 Continued
What is the event F of showing at least two heads? F = {HHH, HHT, HTH, THH} What is the event G of showing no heads? G = {TTT}

11. Example 3
If you flip a coin, what is the theoretical probability that it lands with heads up?
If you flip a coin, what is the theoretical probability that it lands with tails up?
How would you find experimental probability?

12. Example 4
If you roll a standard die, what is the theoretical probability that it lands with the 3 facing up?
If you roll a standard die, what is the theoretical probability that it lands with the 3 or the 4 facing up?

13. Example 5
Suppose we select, without looking, one marble from a bag containing 4 red and 9 purple marbles. What is the probability of selecting a red marble?

14. Example 6
What is the probability of getting a sum of 5 when you roll a pair of dice? (Hint: make a chart!)

15. Rolling a Pair of Dice

16. Example 7: Your Turn!
What is the probability of choosing, at random, the ace of spades from a deck of 52 cards?
What is the probability of choosing any ace from a deck of 52 cards?
What is the probability of drawing a red card from a deck of 52 cards?
What is the probability of drawing a club from a deck of 52 cards?

17. Probability of Multiple Events
So far, we’ve been considering one event at a time. Now, we are going to consider the probability of multiple events.

18. Example 8
A five-card poker hand is drawn from a standard deck of 52 cards. What is the probability that all five cards are spades? How many events are there?

19. Probability of Multiple Events
To find the probability of multiple events, use: THE FUNDAMENTAL COUNTING PRINCIPLE!
Keep doing this for all the events that occur
Probability of the first event
Probability of the second event
Probability of the third event

20. Example 9
A bag contains 20 tennis balls, four of which are defective. If two balls are selected at random from the bag, what is the probability that both are defective?