2. E Birbeck 7/04 Edbirbeck@yahoo.com Simple Probability Definition: Probability : the chance some event will happen. It is the ratio of the number of ways an event can occur to the number of possible outcomes. # of ways a certain outcome can occur # of possible outcomes Probability =

3. E Birbeck 7/04 Edbirbeck@yahoo.com Odds versus Probability Chances of success Chances of failure Odds of success = The ratio for odds uses chances of success and chances of failure…not the total number of outcomes. Chances of failure Chances of success Odds of failure =

4. E Birbeck 7/04 Edbirbeck@yahoo.com Odds versus Probability Chances of success Chances of failure Odds of success = Chances of failure Chances of success Odds of failure = # of ways a certain outcome can occur # of possible outcomes Probability =

5. E Birbeck 7/04 Edbirbeck@yahoo.com Practice : What is the probability of rolling a factor of 6 on a six sided die? A six sided die is labeled 1,2,3,4,5,6 A factor of 6 is a whole number that divides evenly into 6 Know: Factors of 6 1 x 6 = 6 2 x 3 = 6 1, 2, 3, 6 # of ways a certain outcome can occur # of possible outcomes Probability =

6. E Birbeck 7/04 Edbirbeck@yahoo.com Practice : What is the probability of rolling a factor of 6 on a six sided die? A six sided die is labeled 1,2,3,4,5,6 A factor of 6 is a whole number that divides evenly into 6 Know: Factors of 6 1 x 6 = 6 2 x 3 = 6 1, 2, 3, 6 # of ways a certain outcome can occur # of possible outcomes Probability = 4 ways

7. E Birbeck 7/04 Edbirbeck@yahoo.com Practice : What is the probability of rolling a factor of 6 on a six sided die? A six sided die is labeled 1,2,3,4,5,6 A factor of 6 is a whole number that divides evenly into 6 Know: Factors of 6 1 x 6 = 6 2 x 3 = 6 1, 2, 3, 6 4 ways 4 # of possible outcomes Probability =

8. E Birbeck 7/04 Edbirbeck@yahoo.com Practice : What is the probability of rolling a factor of 6 on a six sided die? A six sided die is labeled 1,2,3,4,5,6 A factor of 6 is a whole number that divides evenly into 6 Know: Factors of 6 1 x 6 = 6 2 x 3 = 6 1, 2, 3, 6 4 ways 4 # of possible outcomes Probability = 6 outcomes

9. E Birbeck 7/04 Edbirbeck@yahoo.com Practice : What is the probability of rolling a factor of 6 on a six sided die? A six sided die is labeled 1,2,3,4,5,6 A factor of 6 is a whole number that divides evenly into 6 Know: Factors of 6 1 x 6 = 6 2 x 3 = 6 1, 2, 3, 6 4 ways 4 # of possible outcomes # of possible outcomes Probability = 6 outcomes

10. E Birbeck 7/04 Edbirbeck@yahoo.com Practice : What is the probability of rolling a factor of 6 on a six sided die? A six sided die is labeled 1,2,3,4,5,6 A factor of 6 is a whole number that divides evenly into 6 Know: Factors of 6 1 x 6 = 6 2 x 3 = 6 1, 2, 3, 6 4 ways 4 6 Probability = 6 outcomes

11. E Birbeck 7/04 Edbirbeck@yahoo.com 4 6 Probability = What is the probability of rolling a factor of 6 on a six sided die? Question Simplify 4 6 = 2 3 The probability of rolling a factor of 6 on a six sided die is. 2 3

12. E Birbeck 7/04 Edbirbeck@yahoo.com Two out of three times that you roll the dice, you should roll a factor of 6. 66.6% 67% of the time you should roll a factor of 6. What does that mean?

13. E Birbeck 7/04 Edbirbeck@yahoo.com What does that mean? Two out of three times that you roll the dice, you should roll a factor of 6. 66.6% 67% of the time you should roll a factor of 6.

14. E Birbeck 7/04 Edbirbeck@yahoo.com Sample Space Definition: Sample Space : the set of all possible outcomes Sample Space is used to create a chart or table to solve the problem. When flipping a coin, the sample space is heads or tails. heads tails

15. E Birbeck 7/04 Edbirbeck@yahoo.com Practice : Playing Monopoly or Backgammon, you get to roll again if you roll doubles. What is the probability of rolling doubles? # of ways a certain outcome can occur # of possible outcomes Probability = Know: Solve: Each die has 6 sides Make a table showing all the combinations that you could roll on a pair of dice as ordered pairs.

16. E Birbeck 7/04 Edbirbeck@yahoo.com 1 2 3 4 5 6 1 2 3 4 5 6 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) F i r s t d i e Second die Sample Space for Rolling two Die

17. E Birbeck 7/04 Edbirbeck@yahoo.com 1 2 3 4 5 6 123456123456 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) FirstdieFirstdie Second die Sample Space for Rolling two Die There are 6 ways to get doubles. There 36 possible outcomes.

18. E Birbeck 7/04 Edbirbeck@yahoo.com There are 6 ways to get doubles. There 36 possible outcomes. # of ways a certain outcome can occur # of possible outcomes Probability =

19. E Birbeck 7/04 Edbirbeck@yahoo.com There are 6 ways to get doubles. There 36 possible outcomes. # of ways a certain outcome can occur # of possible outcomes Probability =

20. E Birbeck 7/04 Edbirbeck@yahoo.com There are 6 ways to get doubles. There 36 possible outcomes. 6 # of possible outcomes Probability =

21. E Birbeck 7/04 Edbirbeck@yahoo.com There are 6 ways to get doubles. There 36 possible outcomes. 6 # of possible outcomes Probability =

22. E Birbeck 7/04 Edbirbeck@yahoo.com There are 6 ways to get doubles. There 36 possible outcomes. 6 36 Probability =

23. E Birbeck 7/04 Edbirbeck@yahoo.com There are 6 ways to get doubles. There 36 possible outcomes. 6 36 Probability = Simplify 6 36 = 1 6 What is the probability of rolling doubles? Question: The probability of rolling doubles is. 1 6

24. E Birbeck 7/04 Edbirbeck@yahoo.com The probability of an event is always between 0 and 1, inclusive. If an event cannot happen, its probability is 0. If something is certain to happen, its probability is 1 01 1 2 impossiblecertain50-50 chance

25. E Birbeck 7/04 Edbirbeck@yahoo.com 01 1 2 impossiblecertain50-50 chance 100% 50% 0%

26. E Birbeck 7/04 Edbirbeck@yahoo.com Probability # of ways a certain outcome can occur # of possible outcomes Probability = The probability of an event is always between 0 and 1 or 0-100%. Odds and Probability are expressed differently. * * *

27. E Birbeck 7/04 Edbirbeck@yahoo.com Practice: In Scrabble, each player chooses seven letter tiles. The 100 tiles are in the distribution table below. a) Find the probability of selecting an E if no tiles have been chosen. # of tilesLetters 1J, K, Q, X, Z B, C, F, H, M, P, V, W, Y, blank G D,L,S,U N,R,T O A,I E 2 3 4 6 8 9 12 Know: There are 12 E tiles and 100 tiles in all. P(selecting an E) = 12 100 or 3 25

28. E Birbeck 7/04 Edbirbeck@yahoo.com b) Find the probability of selecting an M if 28 tiles have been chosen and one of them was an M. # of tilesLetters 1J, K, Q, X, Z B, C, F, H, M, P, V, W, Y, blank G D,L,S,U N,R,T O A,I E 2 3 4 6 8 9 12 Scrabble Breakdown Know: There are 2 M tiles. 1 has been selected, so 1 positive outcome remains. P(selecting an M) = 1 72 There are 100 - 28 = 72 tiles left (72 possible outcomes).

29. E Birbeck 7/04 Edbirbeck@yahoo.com c) Find the probability of selecting an X if 42 tiles have been chosen and one of them was an X. # of tilesLetters 1J, K, Q, X, Z B, C, F, H, M, P, V, W, Y, blank G D,L,S,U N,R,T O A,I E 2 3 4 6 8 9 12 Scrabble Breakdown Know: There is only 1 X tile. 1 has been selected, so 0 positive outcomes remain. P(selecting an X) = 0 58 There are 100 - 42 = 58 tiles left (58 possible outcomes). or 0

30. E Birbeck 7/04 Edbirbeck@yahoo.com P(selecting an E) = 12 100 or 3 25 Convert the fractions to percents. P(selecting an M) = 1 72 P(selecting an X) = 0 58 or 0 12% 0% impossible

31. E Birbeck 7/04 Edbirbeck@yahoo.com Convert the fractions to percents. 1 72 P(selecting an M) = 1.4% 1 ÷ 72 means 1 ÷ 72 = 0.0138 = 1.38%= 1.4%

32. E Birbeck 7/04 Edbirbeck@yahoo.com P(selecting an E) = 12 100 or 3 25 Convert the fractions to percents. P(selecting an M) = 1 72 P(selecting an X) = 0 58 or 0 12% 0% impossible 1 ÷ 72 1.4%

33. E Birbeck 7/04 Edbirbeck@yahoo.com Probability # of ways a certain outcome can occur # of possible outcomes Probability = The probability of an event is always between 0 and 1 or 0-100%. Odds and Probability are expressed differently. * * *

34. E Birbeck 7/04 Edbirbeck@yahoo.com Probability # of ways a certain outcome can occur # of possible outcomes Probability = The probability of an event is always between 0 and 1 or 0-100%. Odds and Probability are expressed differently. * * *

35. E Birbeck 7/04 Edbirbeck@yahoo.com