Probability+of+Multiple+Events+-+Independent+Events

Directions: 1. Read the notes below and write down the important information in your notes. 2. Answer the following questions and email your responses to teganolympus@gmail.com: a) Compare and contrast finding the probability of a single event and finding the probability of multiple events. Give at least 2 similarities and at least 2 differences. b) How can you tell if two events are independent events? c) Give an example of 2 independent events. Please do not use an example used in the notes. 3. Open the document "Probability of Independent Events Practice" and complete the problems. Show all your work. Turn in your work during class.



When we talked about probability in the previous lesson, we were talking about one event that was occurring. In this lesson, we will talk about situations in which more than one event is occurring. When we have multiple events occurring at once, they can either be independent or dependent. This lesson will discuss **independent events** and the next will discuss dependent events.
 * NOTES:**


 * Independent Events =** 2 or more events in which what happens in one event DOES NOT affect what happens in the next event. The events have NO IMPACT on one another.

Example 1: Flipping a coin twice. The two events are the first flip and the second flip. The sample space for the first event (the first flip) is {heads, tails}. Regardless of what happens on the first flip, the sample space for the second event (the second flip) is {heads, tails}.

Example 2: Choosing 2 marbles from a bag on after another with replacement. The two events in this situation are choosing the first marble and choosing the second marble. The words "with replacement" mean that you choose the first marble, then put the marble back into the bag. This re-creates the same conditions for the second event as there were in the first. Therefore, what was chosen in the first event DOES NOT affect what can be chosen in the second even.

//Important Fact:// The words **"with replacement"** always indicated **independent events**


 * How can we find the probability of multiple independent events?**

To find the probability of multiple independent events occurring, you **find the probability of each event occurring individually** and then **multiply** those probabilities together.

Say we're trying to find the probability of both outcome A occurring and outcome B occurring (and A and B are independent events), we find the probability of outcome A occurring and then multiply it by the probability of outcome B occurring as shown below:

P(A and B) = P(A) x P(B)

//Example 1:// Selena and Tracey play on a softball team. Selena has 8 hits out of 20 times at bat and Tracey has 6 hits out of 16 times at bat. Based on their past performance, what is the probability that both girls will get a hit next time at bat?

The events that are occurring in this problem are: Selena's at bat and Tracey's at bat These events are independent because what happens during one girl's at bat does not affect what happens during the other girl's at bat.

P(Selena and Tracey hit) = P(Selena hits) x P(Tracey hits) =

//Example 2:// The probability that the Yankees will win their first game is 1/3. The probability that the Mets will win their first game is 3/7. What is the probability that both teams will win their first game?

There are two events occurring here: Yankee's first game and Met's first game These events are independent because what happens during one team's first game does not affect what happens during the other team's first game.