Simple Probability Definition Probability the chance some event

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. Probability = E Birbeck 7/04 Edbirbeck@yahoo. com # of ways a certain outcome can occur # of possible outcomes

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

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

Practice: What is the probability of rolling a factor of 6 on a six sided die? Know: • 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 1 x 6=6 2 x 3=6 Probability = E Birbeck 7/04 Edbirbeck@yahoo. com Factors of 6 1, 2, 3, 6 # of ways a certain outcome can occur # of possible outcomes

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

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

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

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

Question What is the probability of rolling a factor of 6 on a six sided die? Probability = Simplify 4 6 4 2 = 6 3 The probability of rolling a factor of 6 on a 2 six sided die is. 3 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. 6% 67% of the time you should roll a factor of 6. 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 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? Know: Probability = # of ways a certain outcome can occur # of possible outcomes Each die has 6 sides Solve: Make a table showing all the combinations that you could roll on a pair of dice as ordered pairs. E Birbeck 7/04 Edbirbeck@yahoo. com

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

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

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

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

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

There are 6 ways to get doubles. There 36 possible outcomes. Probability = 6 36 Question: What is the probability of rolling doubles? Simplify 6 1 = 36 6 The probability of rolling doubles is 1. 6 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 0 impossible E Birbeck 7/04 Edbirbeck@yahoo. com 1 2 1 50 -50 chance certain

0 1 2 1 impossible 50 -50 chance certain 0% 50% 100% E Birbeck 7/04 Edbirbeck@yahoo. com

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

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. Know: There are 12 E tiles and 100 tiles in all. 12 3 P(selecting an E) = or 100 25 E Birbeck 7/04 Edbirbeck@yahoo. com # of tiles 1 2 3 4 6 8 9 12 Letters J, 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

b) Find the probability of selecting an M if 28 tiles have been chosen and one of them was an M. Know: There are 2 M tiles. 1 has been selected, so 1 positive outcome remains. There are 100 - 28 = 72 tiles left (72 possible outcomes). P(selecting an M) = E Birbeck 7/04 Edbirbeck@yahoo. com 1 72 Scrabble Breakdown # of tiles 1 2 3 4 6 8 9 12 Letters J, 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 c) Find the probability of selecting an X if 42 tiles have been chosen and one of them was an X. # of tiles 1 2 3 4 6 8 9 12 Know: There is only 1 X tile. 1 has been selected, so 0 positive outcomes remain. There are 100 - 42 = 58 tiles left (58 possible outcomes). P(selecting an X) = E Birbeck 7/04 Edbirbeck@yahoo. com 0 58 or 0 Letters J, 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

$Convert the fractions to percents. 12 P(selecting an E) = 100 P(selecting an M)$

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

$Convert the fractions to percents. 1. 4% P(selecting an M) = 1 72 means$

Convert the fractions to percents. 1. 4% P(selecting an M) = 1 72 means 1 ÷ 72 = 0. 0138 = 1. 38% = 1. 4% E Birbeck 7/04 Edbirbeck@yahoo. com

$Convert the fractions to percents. 12 P(selecting an E) = 100 P(selecting an M)$

Convert the fractions to percents. 12 P(selecting an E) = 100 P(selecting an M) = 1 72 P(selecting an X) = 0 58 E Birbeck 7/04 Edbirbeck@yahoo. com 3 or 25 1 ÷ 72 or 0 12% 1. 4% 0% impossible

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

E Birbeck 7/04 Edbirbeck@yahoo. com