Probability What do you think probability means? ◦Write down a definition based on what you already know ◦Use the word probability in a sentence.

Example: Describing Likelihood

Apophis Upon its discovery in 2004, Apophis was briefly estimated to have a 2.7% chance of impacting the Earth in Additional measurements later showed that there was no impact risk at that time from the object. However, there will be a historically close approach to the Earth, estimated to be a 1 in 800 year event.

Target 12.1 I can identify and count the outcomes of an experiment and calculate the theoretical probability of an event.

Sample Space I am going to flip a coin. What are the possible outcomes? How many total possible outcomes are there? ◦The set of all of the possible outcomes is called the sample space What is the probability that the coin will land on tails?

Sample Space – set(list) of all possible outcomes. Sample space: HH, HT, TH, TT

The probability of an event is a number between 0 and 1 that measures the likelihood that an event will occur.

The probability of an event is a number between 0 and 1 that measures the likelihood that an event will occur.

 To find theoretical probability we use mathematical reasoning  To find experimental probability we run an experiment Theoretical vs Experimental Probability:

 To find theoretical probability we use mathematical reasoning  To find experimental probability we run an experiment Theoretical vs Experimental Probability:

what we want what we can get

Example 1 6- sided die What is the probability of rolling an even number? What is the probability of rolling a multiple of 3? What is the probability of rolling number greater than 2? What is the probability of rolling a 7?

Example sided die What is the probability of rolling an even number? What is the probability of rolling a multiple of 3? What is the probability of rolling number greater than 2? What is the probability of rolling a 7?

Example sided dice P(Sum=6)= P(Sum  6)= P(Sum>9)= P(Sum<9)=

Complement of an Event You roll a die. What is the probability that 2 will not appear on the die? Ray and Shan are playing football. Probability of Ray winning the football game is.36. So what is the probability of Shan winning? A bowl contains 5 green, 6 blue, and 9 red stones. If a stone is chosen at random from the bowl, what is the probability that it is not green?

Complement of an Event - all of the possible outcomes in the sample space that are not part of the event. P(event)+P(not event) = 1 P(not event)=1 - P(event)

Complement of an Event When the event is Heads, the complement is Tails When the event is {Monday, Wednesday} the complement is {Tuesday, Thursday, Friday, Saturday, Sunday} So the Complement of an event is all the other outcomes (not the ones we want). And together the Event and its Complement make all possible outcomes. When the event is rolling a 5, the complement is not rolling a 5

Example 4 The probability of not getting a 5 would be:

Homework p.672 C: #1-4, 9-12, 18, 22 B: #4, 9-12, 15, 17, 18 A: #4, 9-12, 17, 22, 24

Theoretical vs Experimental Probability:

Example 5 Find the theoretical probability of rolling each sum