The document discusses probability concepts such as outcomes, events, theoretical probability, probability as a percent, complements of events, sample spaces, and using tree diagrams to calculate probabilities of outcomes. It provides examples of calculating probabilities using the formula for theoretical probability and explains how to determine complements and sample spaces. It also presents a tree diagram example of calculating the probability of having at least two girls in a family with three children.

1. More Probability

2. Outcomes Possible results of an experiment. This is compared to an event which is any group of outcomes.

3. The formula (again) P (event) = number of favorable outcomes number of possible outcomes Using this formula gives us theoretical probability .

4. Probability as a percent Let’s say we have a 1/5 probability of having pizza served for lunch. 1/5 = .2 = 20% There is a 20% probability we will have pizza for lunch.

5. Probability as a percent Probabilities range from 0% to 100% 0% is an impossible event Like getting a black m&m in an Easter package 100% is a certain event Like getting a pastel m&m in an Easter package 50% would be the probability of getting a yellow m&m when there are only yellow and green m&ms to get.

6. Complement of an event These are the outcomes that won’t happen in the event. The experiment involves rolling a die. P(4)=1/6 What is the probability you won’t roll a 4? 5/6 1 – 1/6 = 5/6

7. Complement of an event P(even)= ½ What is it’s complement? ½ P(#<5)= 4/6=2/3 What is it’s complement? 2/6=1/3

8. Sample Space Set of all possible outcomes Sometimes you have to display the outcomes using a tree diagram What is the probability that there are at least two girls in a family of three children?

9. Tree Diagram 1st Child 2nd Child 3rd Child Sample Space G B G B G B G B G B G B G B GGG GGB GBB GBG BGG BGB BBG BBB

10. Tree Diagram How many outcomes are there that have 2 girls in them P(at least 2 girls)= 4/8 = ½ P(exactly 2 girls)= 3/8 Sample Space GGG GGB GBB GBG BGG BGB BBG BBB