L6-Counting Methods and Techniques in an Experiment.pptx

grade 8 math presentation

1. MAGANDANG ARAW! Mathematics 8

2. GUESS THE PICTURE!

3. Stratified sampling involves dividing the population into subgroups or strata based on certain characteristics that are relevant to the research. Random samples are then taken from each stratum, ensuring representation from all segments of the population. This method is useful when there are distinct subgroups with different characteristics. Stratified Sampling

4. Stratified Sampling EXAMPLE Suppose a company wants to assess job satisfaction among its employees. Instead of randomly selecting employees, the company could first divide employees into strata based on departments (e.g., marketing, finance, operations). The company would then randomly sample employees from each department to ensure representation from all areas.

5. Counting Methods and Techniques in an Experiment

6. It involves identifying the outcomes, then listing and counting them. Examples: Drawing a card labelled with the seasons of the year. S={winter, spring, summer, fall} n(S)=4 Systematic Listing

7. E= {king of hearts, king of spades, king of diamonds, king of clubs} n(E)=4 Drawing a king from a standard deck of 52 cards Getting an odd number from rolling an octahedral die E={1, 3 , 5, 7} n(E)=4

8. Counting the Outcomes of Experiment Using Tables and Tree Diagrams

9. EXAMPLE 1 Vien is ordering a pizza. The pizza shop offers customers a choice of Hawaiian, pepperoni, or cheese on either regular or thin crust. How many different combinations of toppings and crust are possible? Let H represent hawaiian , P for pepperoni, C for cheese, R for regular, and T for thin.

10. Method 1: Using a table This method uses columns and rows where to enter all possible outcomes of an experiment. 6 Possible outcomes     Flavor Crust   Regular Thin Hawaiian HR HT Pepperoni PR PT Cheese CR CT

11. Method 2: Tree Diagram It consists of line segments coming from a starting point to the outcome point. All possible outcomes are visually represented by the branches. 6 Possible outcomes There are 6 possible outcomes or combinations of pizza.

12. Example 2: List the possible outcomes using a Table In a debate contest, the participants are divided into two groups so that members of Group 1 will be paired with members of Group 2. The members of Group 1 are Elena, Estela, Felisa, and Mae while the members of Group 2 are Mark, Red, and Sam. The number of possible pairings is shown in the table below.

13.   Rose May Jane Keith Mark Mark, Rose Mark, May Mark, Jane Mark, Keith Ken Ken, Rose Ken, May Ken, Jane Ken, Keith John John, Rose John, May John, Jane John, Keith 12 Possible outcomes Counting Outcomes using Table

14. 4 Possible outcomes Counting Outcomes using Tree Diagram

15. If event can occur in n1 ways and is followed by event 2 that can occur in n2 ways, then the total number of ways in which both events can occur is n1 × n2. Fundamental Counting Principle

16. Example 1: Potato Corner offers four different flavors of fries, three container sizes, and three dips. How many different ways can one customer order fries? Solution: Event 1 (choosing a flavor) can occur in 4 ways, event 2 (choosing a container size) in 3 ways, and event 3 (choosing a dip) in 3 ways. n(E)= n1 × n2 × n3 = 4 × 3 × 3 = 36 different ways of ordering fries.

17. Example 2: How many possible outcomes are there if a die is rolled once and a coin is tossed once? Solution: The event rolling a die once has six possible outcomes while the event tossing a coin once has two possible outcomes. n(E)= n1 × n2 = 6 × 2 = 12 possible outcomes when a die is rolled once, and a coin is tossed once.

18. ACTIVITY: WHAT’S MY OUTFIT?

19. Instruction: The teacher will divide the class into five groups. Each group will help Reign to choose an outfit by matching her available jeans and shirts. Work together and list all possible outfit combinations.

20. Capture sampling is a technique commonly used in ecology and biology. It involves capturing and marking a portion of the population, releasing them back into the environment, and then recapturing a new sample later. By comparing the marked and unmarked individuals, researchers can estimate population size and dynamics. Capture Sampling

21. Capture Sampling EXAMPLE In ecology, a researcher studying the population of a specific bird species might capture and tag a sample of birds in a particular area. After releasing the marked birds, the researcher could later recapture a new sample. By comparing the ratio of marked to unmarked birds in the second sample, the researcher can estimate the overall population size.