5-8 Probability and Chance

Probability Probability is a measure of how likely it is for an event to happen.

The probability of an event is always between 0 and 1, inclusive 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 1 2 1 impossible 50-50 chance certain 0% 50% 100%

Vocabulary Probability- P(event) Outcome Event Sample Space How likely it is for an event to occur Outcome The result of a single trial Event Any outcome or group of outcomes in an experiment Sample Space All the possible outcomes

For instance… Let’s use the example of rolling a number cube (like dice). An event could be rolling an even number What’s the sample space? 1, 2, 3, 4, 5, 6 Which are the favorable outcomes? 2, 4, 6

Theoretical Probability Use this formula when… all outcomes are equally likely to occur. P(event) = number of favorable outcomes number of possible outcomes P(rolling an even) = P(rolling a number greater than 2 on a die)

1. What is the probability that the spinner will stop on part A? C D ¼ What is the probability that the spinner will stop on An even number? An odd number? 1/3 3 1 2 2/3 A 3. What fraction names the probability that the spinner will stop in the area marked A? C B 1/3

Probability Questions Lawrence is the captain of his track team. The team is deciding on a color and all eight members wrote their choice down on equal size cards. If Lawrence picks one card at random, what is the probability that he will pick blue? 3/8 blue blue green black yellow blue black red

-You can express probability as a fraction or a percent: Example 2: If a bag contains 1 blue cube, 3 red cubes, and 4 yellow cubes what is the probability of selecting a red cube? -You can express probability as a fraction or a percent: An impossible event would be 0% Event equally likely to happen would be 50% Event certain to happen would be 100% Example of a certain event: having a test on this stuff. Example of an impossible event: having it reach 1000 in January.

-When finding the probability of two events, this or that, add the two probabilities together. Example 3: Find the probability of the following events below. a.) What is the probability of rolling a 6 or a 4 on a dice? b.) What is the probability of rolling an even number on a dice or rolling a 1? c.) What is the probability of not rolling a number greater than 3.

CHILDREN A family has two children CHILDREN A family has two children. Draw a tree diagram to show the sample space of the children’s genders. Then determine the probability of the family having two girls. There are four equally-likely outcomes with one showing two girls. Answer: The probability of the family having two girls is

COINS A game involves flipping two pennies COINS A game involves flipping two pennies. Draw a tree diagram to show the sample space of the results in terms of heads and tails. Then determine the probability of flipping one head and one tail. Answer:

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

Know: Probability = Solve: Each die has 6 sides Practice: Playing Monopoly or Backgammon, you get to roll again if you roll doubles. What is the probability of rolling doubles? Know: # of ways a certain outcome can occur Probability = # 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.

Second die Fi rs t d ie Sample Space for Rolling two Die 1 2 3 4 5 6 1 1 2 3 4 5 6 Fi rs t d ie 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)

Second die Fi rs t d ie Sample Space for Rolling two Die 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) Fi rs t d ie Second die Sample Space for Rolling two Die There are 6 ways to get doubles. There 36 possible outcomes.

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

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

There are 6 ways to get doubles. There 36 possible outcomes. Probability = # of possible outcomes

There are 6 ways to get doubles. There 36 possible outcomes. Probability = # of possible outcomes

There are 6 ways to get doubles. There 36 possible outcomes. Probability = 36

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

CHANCE Chance is how likely it is that something will happen. To state a chance, we use a percent. ½ Probability 1 Equally likely to happen or not to happen Certain to happen Certain not to happen Chance 50 % 0% 100%

Homework Pg. 249 #6-24 even Extra Credit #26 – 4 pts. ec