Make and use sample spaces and use the counting principle.

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Presentation transcript:

Make and use sample spaces and use the counting principle.

Sample space All possible outcomes Used to find the probability of an event. Ex: create a table to find the sample space for rolling 2 dice. Outcomes are written as ordered pairs. There are 36 possible outcomes P(at least one 3) There are 11 possibilities P(at least one 3)= 11 36

Using a Tree Diagram Suppose you are going to travel on a river. There are 2 choices for boats-- a kayak and a rowboat. There are three streams to follow-- north, northwest, and northeast. 6 possible outcomes. What is the probability of taking a kayak directly north? 1 6

Counting Principle When rolling 2 dice we had 36 possible outcomes 6 choices for the 1st die and 6 for the 2nd. Notice that 6×6 = 36, the size of the sample space When choosing a river trip we had 6 possible outcomes 2 choices for a boat and 3 for direction Notice that 2×3 = 6, the size of the sample space So, the counting principle says that if there are 𝑚 ways of making a first choice and 𝑛 ways to make a second choice, then there are 𝑚×𝑛 ways to make both choices.

Practice How many different sandwiches can you order when you choose one bread and one meat from the menu? 5 bread choices 6 meat choices 5×6=30 sandwich choices If chicken is added to list of meats on the menu, how many sandwiches are now available? 35

Assignment Odds P.321 #11-27