Probability and Chance Mr. Calise

Probability Probability is a measure of how likely it is for an event to happen. We name a probability with a number from 0 to 1. If an event is certain to happen, then the probability of the event is 1. If an event is certain not to happen, then the probability of the event is 0.

Probability If it is uncertain whether or not an event will happen, then its probability is some fraction between 0 and 1 (or a fraction converted to a decimal number).

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

Probability Activity In your group, open your M&M bag and put the candy on the paper plate. Put ten brown M&Ms and five yellow M&Ms in the bag. Ask your group, what is the probability of getting a brown M&M? Ask your group, what is the probability of getting a yellow M&M?

Examples Another person in the group will then put in 8 green M&Ms and 2 blue M&Ms. Ask the group to predict which color you are more likely to pull out, least likely, unlikely, or equally likely to pull out. The last person in the group will make up his/her own problem with the M&Ms.

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? blue blue green black yellow blue black red

Donald is rolling a number cube labeled 1 to 6 Donald is rolling a number cube labeled 1 to 6. Which of the following is LEAST LIKELY? an even number an odd number a number greater than 5

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%

Chance When a meteorologist states that the chance of rain is 50%, the meteorologist is saying that it is equally likely to rain or not to rain. If the chance of rain rises to 80%, it is more likely to rain. If the chance drops to 20%, then it may rain, but it probably will not rain.

1 2 1. What is the chance of spinning a number greater than 1? 4 3 What is the chance of spinning a 4? What is the chance that the spinner will stop on an odd number? 4 1 2 3 5 4. What is the chance of rolling an even number with one toss of on number cube?

DRILL What is the probability of rolling a number less than 5 on a 6-sided die? What is the theoretical probability of getting a green marble, if there is a bag with 16 blue marbles, 18 green marbles, 14 yellow marbles and 16 orange marbles? What is the experimental probability of rolling a 3 given: {2, 3, 4, 1, 3, 4, 6, 5, 2, 3, 3, 4, 1, 6}

Algebra I Experimental vs. Theoretical Probability

Theoretical Probability The theoretical probability of an event is the “actual” probability of something happening. Number of “correct” outcomes divided by the total number of outcomes.

Experimental Probability The experimental probability of an event is the probability of an event based on previous outcomes. Example: If you flipped a coin 10 times and got { T, T, H, T, H, H, H, T, T, T} The experimental probability of getting tails is 6 out of 10 or 3/5.

Example {2, 4, 1, 6, 5, 1, 1, 4, 5, 3, 2, 3, 6, 6} {1, 4, 5, 5, 3, 3, 6, 2, 6, 6, 2, 3, 4, 1} {2, 3, 2, 2, 5, 6, 1, 2, 3, 4, 3, 2, 2, 6}

Calculator Activity * We are going to simulate rolling a die 50 times using the calculators and then calculate the theoretical probability and experimental probability of the event.

Homework Write five events and say what the theoretical probability and experimental probability of the events are. Ex: {1, 4, 3, 5, 5, 2, 3, 1, 6, 2, 2} Theoretical Prob of rolling a 2 is 1/6 Experimental Prob of rolling a 2 is 3/11

DRILL What is the probability of rolling an odd number on a 6-sided die? What is the probability of getting a green marble, if there is a bag with 6 blue marbles, 5 green marbles, 3 yellow marbles and 8 orange marbles? What is the probability of not getting a blue or yellow marble from the same bag?

Tree Diagram Is a method used for writing out all the possible outcomes for multiple events.

Sample Space The sample space is the set of all possible outcomes for a given event. Example: The sample space for rolling a die is {1, 2, 3, 4, 5, 6}

Counting Principle If two or more events occur in x and y ways to find the total number of combinations (choices) you simply multiply the number of possible outcomes in each group by each other. Example: If you have 4 shirts, 3 pairs of pants, 2 pairs of shoes and 3 hats, you can make 4(3)(2)(3) different outfits. Which gives you a total of 72 outfits.

Factorial Is used when you want to figure out how many ways “n” number of objects can be arranged. The symbol for factorial is an exclamation point. (n!) Factorial means to multiply by every number less then “n” down to 1. Example: 5! = 5(4)(3)(2)(1)

DRILL What is the probability of rolling a number less than 5 on a 6-sided die? What is the probability of getting a green marble, if there is a bag with 4 blue marbles, 3 green marbles, 4 yellow marbles and 9 orange marbles? What is the probability of not getting a green or yellow marble from the same bag?