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19. Probability. a. SERRA

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**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: Example 1: Do it & check your answers. Exercise 19A: 1,3 Probability investigation (drawing pins, coins, dice, paper clips…) you choose. 1/2/3 Pages Extra: do a second/third investigation.

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**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: Examples 1,2,3 : Do them & check your answers. Exercise 19B: 1b, 2b, 3b Extra c’s and d’s

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**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: Examples 4 and 5: Do them & check your answers. Exercise 19C: 1,5,9 Extra: Even numbers Time for investigations? Online portfolio?

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**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: Examples 6, 7 and 8: Do them & check your answers. Exercise 19D: 3 Exercise 19 E1: 3,5 Exercise 19 E2: 1,3 Extra: Even numbers

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**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: Examples 11, 12 and 13: Do them & check your answers. Exercise 19F: 1 and 3. Exercise 19G: 1 and 9 Extra: Even numbers

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**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. Individual work: Exercise 19H: 1 (part of it done in class), 3 and 7 Extra: Even numbers Video: Exercise 19H5. Page 493.

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**19I. Sets and Venn diagrams.**

Class work: Review: Sample space, union, intersection, complementary, disjoint sets. Individual work: Examples : Do them & check your answers. Exercise 19I: 3,9,11 Extra: Even numbers Remember 3rd investigation!!!!!

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**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: Examples 21-25: Do them & check your answers. Exercise 19J: 3,5 and 9 (happy idea) or 11 (organized) . Extra: Even numbers

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**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: Examples 26 and 27: Do them & check your answers. Exercise 19K: 1,3,5 Extra: Even numbers

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Review unit 19 INDIVIDUAL WORKHOMEWORK 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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