Probability

1. Probability Data, Stats, and Probability

2. Probability Impossible Possible but not certain Certain Probability 0 Probability between 0 and 1 Probability 1 What are some events that have a probability of 1? What are some events that have a probability of 0?

3. Probability The probability that an event will happen is given by the following formula: number of favorable outcomes P (event) = total number of outcomes

4. Probability A bag contains the following: 7 red marbles 6 green marbles 7 white marbles What is the probability of selecting a red marble? 7 red marbles 7 number of favorable outcomes P (red) = = 20 total marbles total number of outcomes 20

5. Probability Two numbered cubes are rolled. What is the probability that the sum of their numbers will be equal to 7? 6 1 P(7)= = How can their sum equal 7? 36 6 1 and 6 2 and 5 3 and 4 6 and 1 5 and 2 4 and 3 How many total outcomes are there when you roll two numbered cubes? 6 for Cube 1 6 for Cube 2 = 36 total

6. Probability For the pair of spinners below, draw a tree diagram showing the outcomes when spinner 1 is spun and spinner 2 is spun. 1 2 1 2 3 4 3

7. Probability 1 2 1 2 3 4 3 If both spinners are spun, what is the probability that the sum will equal 5? P (sum equals 5) =

8. Probability If the probability of an event is 0, then: It is certain It is impossible It is probable but not certain It is probable but not impossible

9. Probability The probability the sun sets in the west is: a) 0 b) 1 c) -1 d) ½

10. Probability Data, Stats, and Probability

11. Probability Worksheet from yesterday: Lesson 8.1 practice (1-25 odd)

12. Probability If you flip a coin, what is the probability that it lands on either heads or tails? This is an example of an “or” statement

13. Probability “Or” statements: An “or” statement will increase the number of favorable outcomes without increasing the total number of outcomes → increases the probability of an event

14. Probability Suppose you roll a pair of numbered cubes. What is the probability that the two numbers are equal or their sum equals 7? Sum = 7 Equal: 6 and 1 12 1 and 1 Prob. = 2 and 2 1 and 6 36 3 and 3 2 and 5 1 = 4 and 4 5 and 2 3 5 and 5 3 and 4 4 and 3 6 and 6

15. Probability Suppose you select a card at random from a standard deck of cards. Find the probability that it is: 1 P (ace of spades) = 52 13 1 P (heart) = = 52 4 14 7 = P (heart or ace of spades) = 52 26

16. Probability Data, Stats, and Probability

17. Probability Worksheet from yesterday: Lesson 8.2; 5 - 14

18. Probability • Probability of multiple events • If you flip a coin, what is the probability that the coin will land on heads? • If you flip the coin again, what is the probability that it will land on heads again? • What is the probability of flipping a coin twice and having it land on heads twice?

19. Probability When you are finding the probability of multiple events: Find the probability of each event separately Multiply the two probabilities together Reduce to lowest terms

20. Probability You flip a coin and roll a numbered cube. What is the probability of the coin landing on tails and the numbered cube landing on 4? P (tails) = P (4) = P (tails & 4) =

21. Probability You pick two cards at random from a standard deck of cards without replacing them. What is the probability that you pick a red card followed by a black card? P (red) = P (black) = P (red, black) =

22. Probability A deck of cards has 4 orange, 5 pink, and 5 yellow cards. You pick 3 cards from the deck. Cards are not returned to the deck after they are picked. What is the probability the first card is yellow, the second card is pink, and the third card is orange? P (y.) = P (p.) = P (o.) = P (y,p,o) =

23. Probability Classwork / homework if you do not finish: Worksheet on probability of single and multiple events.