Fundamental counting principle PPT LESSON 2
- 2. REVIEW Situation Maria tossed a coin and wanted a tail Juan rolls a die and wants to get numbers below 4 Experiment Outcome Sample Space Event Sample space of event No. of sample space of event 𝑻𝒐𝒔𝒔𝒊𝒏𝒈 𝒂 𝒄𝒐𝒊𝒏 𝑹𝒐𝒍𝒍𝒊𝒏𝒈 𝒂 𝒅𝒊𝒆 𝑯𝒆𝒂𝒅 𝒐𝒓 𝑻𝒂𝒊𝒍 𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔 𝒘𝒂𝒏𝒕𝒆𝒅 𝒂 𝒕𝒂𝒊𝒍 𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒃𝒆𝒍𝒐𝒘 𝟒 𝑺 = {𝑯𝒆𝒂𝒅 , 𝑻𝒂𝒊𝒍} 𝑺 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔} 𝑺 𝑬𝒗𝒆𝒏𝒕 = {𝟏, 𝟐, 𝟑} 𝑺 𝑬𝒗𝒆𝒏𝒕 = {𝑻𝒂𝒊𝒍} 𝟏 𝟑
- 4. In a tournament of 2 vs 2, you need to use one fighter and one marksman how many possible pairs of choosing one marksman and one fighter? CLAUD E GRANGE R DYROTT H CHO U CLAUDE AND DYROTTH CLAUDE AND CHOU GRANGER AND DYROTTH GRANGER AND CHOU M A R K S M A N F I G H T E R In this experiment, how did we get the number of possible ways which is 4? 4 ways to choose one marksman and one fighter
- 6. Counts the number of occurrences of an outcome in an experiment: (a) table; (b) tree diagram; (c) systematic listing; and (d) fundamental counting OBJECTIV E
- 7. Table Use to present the set of all possible outcomes or the sample space of an experiment. Tree diagram An illustration consisting of line segments connecting the starting point up to the outcome point. Systematic Listing Writing down in an organized and systematic way to make sure that none of the possible outcomes is missed out. Fundamental Counting Principle States that we can find the total number of ways different event occur by METHODS IN COUNTING POSSIBLE OUTCOMES
- 8. Jericho invited Maria to her party: Maria has 3 Blouses (Stripes with ruffles, long sleeve, and sleeveless) and 3 skirt (red, pink, black) in her closet reserved for such occasions. Assuming that any skirt can be paired with any blouse. In how many ways can Maria select her outfit? EXAMPL E Blouse s Skirt 9 ways can select her outfit BY TABLE
- 9. 9 ways can select her outfit BY TREE DIAGRAM Blouse s Skirt s
- 10. BY SYSTEMATIC LISTING Blouse s Skirt s Stripes with ruffles Long Sleeve Sleeveless Red Skirt Pink Skirt Black Skirt (Stripes with ruffles, Red skirt) (Long sleeve, Red skirt) (Stripes with ruffles, Pink skirt) (Long-sleeve, Pink skirt) (Stripes with ruffles, Black skirt) (Sleeveless, Red skirt) (Long-sleeve, Black skirt) (Sleeveless, Pink skirt) (Sleeveless, Black skirt) 9 ways can select her outfit
- 11. BY FUNDAMENTAL COUNTING PRINCIPLE Blouse s Skirt s 𝟑 9 ways can select her outfit 𝟑 × = 𝟗
- 12. Flipping a coin and rolling a die EXAMPL E BY TABLE Di e Coin 12 possible outcomes
- 13. BY TREE DIAGRAM Flippin g a coin and rolling a die Flipping a coin Rolling a die 𝒏 𝑺 = 𝟏𝟐 Outcomes 𝒉𝒆𝒂𝒅, 𝟏 𝒉𝒆𝒂𝒅, 𝟐 𝒉𝒆𝒂𝒅, 𝟑 𝒉𝒆𝒂𝒅, 𝟒 𝒉𝒆𝒂𝒅, 𝟓 𝒉𝒆𝒂𝒅, 𝟔 𝒕𝒂𝒊𝒍, 𝟏 𝒕𝒂𝒊𝒍, 𝟐 𝒕𝒂𝒊𝒍, 𝟑 𝒕𝒂𝒊𝒍, 𝟒 𝒕𝒂𝒊𝒍, 𝟓 𝒕𝒂𝒊𝒍, 𝟔
- 14. BY SYSTEMATIC LISTING Flipping a coin Rolling a die 𝒏 𝑺 = 𝟏𝟐 Listing the Sample space 𝑺 = { 𝒉𝒆𝒂𝒅, 𝟏 , 𝒉𝒆𝒂𝒅, 𝟐 , 𝒉𝒆𝒂𝒅, 𝟑 , 𝒉𝒆𝒂𝒅, 𝟒 , 𝒉𝒆𝒂𝒅, 𝟓 , 𝒉𝒆𝒂𝒅, 𝟔 , 𝒕𝒂𝒊𝒍, 𝟏 , 𝒕𝒂𝒊𝒍, 𝟐 , 𝒕𝒂𝒊𝒍, 𝟑 , 𝒕𝒂𝒊𝒍, 𝟒 . 𝒕𝒂𝒊𝒍, 𝟓 , 𝒕𝒂𝒊𝒍, 𝟔 𝐻𝑒𝑎𝑑 𝑜𝑟 𝑇𝑎𝑖𝑙 1,2,3,4,5,6 By combining all possible outcomes of coin and a die
- 15. BY FUNDAMENTAL COUNTING PRINCIPLE Determine the possible outcomes Number of possible outcomes COIN DIE HEAD AND TAIL 1,2,3,4,5,6 Count the no. of possible outcomes 2 possible outcomes 6 possible outcomes 2 × 6 12 𝒏 𝑺 = 𝟏𝟐
- 16. A student is choosing between two subjects Science or Math and intend to enroll in at UP, DLSU or ADMU. How many ways can a subject and a school be chosen? By tree diagram and fundamental counting principle LET DO THIS! BY TREE DIAGRAM SUBJE CT SCHOOL OUTCOM E Scien ce Math U P DLS U ADMU U P DLS U ADMU 𝑺𝒄𝒊𝒆𝒏𝒄𝒆, 𝑼𝑷 𝑺𝒄𝒊𝒆𝒏𝒄𝒆, 𝑫𝑳𝑺𝑼 𝑺𝒄𝒊𝒆𝒏𝒄𝒆, 𝑨𝑫𝑴𝑼 𝑴𝒂𝒕𝒉, 𝑼𝑷 𝑴𝒂𝒕𝒉, 𝑫𝑳𝑺𝑼 𝑴𝒂𝒕𝒉, 𝑨𝑫𝑴𝑼 The University of the Philippines (UP) De La Salle University (DLSU) Ateneo de Manila University (ADMU) BY FUNDAMENTAL COUNTING PRINCIPLE 𝟐 𝒔𝒖𝒃𝒋𝒆𝒄𝒕𝒔 𝟑 𝒔𝒄𝒉𝒐𝒐𝒍𝒔 × 𝟔 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝒄𝒉𝒐𝒊𝒄𝒆𝒔
- 17. LET DO THIS! GENETICS: How many possible combinations of blue eyes and brown eyes can be formed from a mother with (blue eyes) and a father with (brown eyes)? bb – BLUE EYES Bb – BROWN EYES PUNETTE SQUARE The Punnett square is a square diagram that is used to predict the genotypes of a particular cross or breeding experiment. Blue eyes Brown eyes 𝐵 𝑏 𝑏 𝑏 𝑩𝒃 𝑩𝒃 𝒃𝒃 𝒃𝒃 𝟒 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝒄𝒐𝒎𝒃𝒊𝒏𝒂𝒕𝒊𝒐𝒏
- 18. Fundamental counting principle It states that we can find the total number of ways different event occur by multiplying the number of ways each event can happen. Other methods in counting possible outcomes? BY TABLE BY TREE DIAGRAM BY SYSTEMATIC LISTING