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19. PROBABILITY. A. SERRA. 19A. Experimental probability. Class work: Why study probability? Case study: life insurance. Experimental probability: trials,

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Presentation on theme: "19. PROBABILITY. A. SERRA. 19A. Experimental probability. Class work: Why study probability? Case study: life insurance. Experimental probability: trials,"— Presentation transcript:

1 19. PROBABILITY. A. SERRA

2 19A. Experimental probability. Class work: Why study probability? Case study: life insurance. Experimental probability: trials, outcomes, frequency, relative frequency = experimental probability. Fathom/ real experiment. Individual work: 1.Example 1: Do it & check your answers. 2.Exercise 19A: 1,3 3.Probability investigation (drawing pins, coins, dice, paper clips…) you choose. 1/2/3 Pages Extra: do a second/third investigation.

3 19B. Sample Space. Class work: The settlers of Catan game. Experimental probability Fathom experiment 2 dice. Representing sample spaces: listing outcomes, 2D Grids, Tree diagrams. Example Exercise 19B: 1a, 2a, 3a Individual work: 1.Examples 1,2,3 : Do them & check your answers. 2.Exercise 19B: 1b, 2b, 3b 3.Extra c’s and d’s

4 19C. Theoretical probability. Class work: Do we need to experiment when equally likely possible results? P(E) = Number (E) / Total number of possible outcomes. P(E) + P(E’) = 1 Individual work: 1.Examples 4 and 5: Do them & check your answers. 2.Exercise 19C: 1,5,9 3.Extra: Even numbers

5 19D & E. Using grids to find probabilities. Compound events. Class work: Case study tossing a coin and a die. Finding P(H&odd) Finding formula P(A and B) for two independent events A and B, using grids. Dependent events (e.g. balls from a box). Individual work: 1.Examples 6, 7 and 8: Do them & check your answers. 2.Exercise 19D: 3 3.Exercise 19 E1: 3,5 4.Exercise 19 E2: 1,3 5.Extra: Even numbers

6 19F&G. Using tree diagrams. Sampling with and without replacement. Class work: Our case study: tossing a coin and a die. Finding P(H&odd). And balls from a bag. Individual work: 1.Examples 11, 12 and 13: Do them & check your answers. 2.Exercise 19F: 1 and 3. 3.Exercise 19G: 1 and 9 4. Extra: Even numbers

7 19H. Pascal’s triangle revisited. Class work: Review: Newton’s (a+b)^n and Pascal’s Triangle. Use in probability (H + T ) ^ n Using TI to calculate elements in Pascal’s Triangle. Example. Exercise 19H5. Page 493.Exercise 19H5. Page 493. Individual work: 1.Exercise 19H: 1 (part of it done in class), 3 and 7 2.Extra: Even numbers

8 19I. Sets and Venn diagrams. Class work: Review: Sample space, union, intersection, complementary, disjoint sets. Individual work: 1.Examples : Do them & check your answers. 2.Exercise 19I: 3,9,11 3.Extra: Even numbers

9 19J. Laws of probability. Class work: From previous section observe: P(A or B) = P(A) + P (B) – P (A and B) P (A/B)= P(Aand B)/P (B) Individual work: 1.Examples 21-25: Do them & check your answers. 2.Exercise 19J: 3,5 and 9 (happy idea) or 11 (organized). 3.Extra: Even numbers

10 19K. Independent events revisited. Class work: From previous section remember: P(A and B) = P(A) P (B) iff independent. Thus P(A/B)= P(A) Individual work: 1.Examples 26 and 27: Do them & check your answers. 2.Exercise 19K: 1,3,5 3.Extra: Even numbers

11 Review unit 19 INDIVIDUAL WORK  HOMEWORK Review Set 19A. (Do, correct your answers and write down score (total and percentage “%”) Mock test: Same Extra: Create an online quiz using Google forms and share it with the group. Please make sure your answers are correct. A positive in homework and/or in professionalism can be awarded if you do this task! Next> Test


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