E Birbeck 7/04 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 =

E Birbeck 7/04 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 =

E Birbeck 7/04 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 =

E Birbeck 7/04 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 =

E Birbeck 7/04 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

E Birbeck 7/04 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 =

E Birbeck 7/04 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

E Birbeck 7/04 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

E Birbeck 7/04 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

E Birbeck 7/ 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

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

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

E Birbeck 7/04 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

E Birbeck 7/04 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.

E Birbeck 7/ (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

E Birbeck 7/ (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.

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

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

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

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

E Birbeck 7/04 There are 6 ways to get doubles. There 36 possible outcomes Probability =

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

E Birbeck 7/04 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 impossiblecertain50-50 chance

E Birbeck 7/ impossiblecertain50-50 chance 100% 50% 0%

E Birbeck 7/04 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. * * *

E Birbeck 7/04 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 Know: There are 12 E tiles and 100 tiles in all. P(selecting an E) = or 3 25

E Birbeck 7/04 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 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 = 72 tiles left (72 possible outcomes).

E Birbeck 7/04 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 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 = 58 tiles left (58 possible outcomes). or 0

E Birbeck 7/04 P(selecting an E) = 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

E Birbeck 7/04 Convert the fractions to percents P(selecting an M) = 1.4% 1 ÷ 72 means 1 ÷ 72 = = 1.38%= 1.4%

E Birbeck 7/04 P(selecting an E) = 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 ÷ %

E Birbeck 7/04 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. * * *

E Birbeck 7/04 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. * * *

E Birbeck 7/04