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Understanding Probability: Activities for Class II.C Students

This CLIL project focuses on teaching probability concepts to Class II.C students through engaging activities. Students will explore key ideas such as likely, probable outcomes, and sample space using relatable examples such as coins and dice. The lessons include both classical and frequentist definitions of probability along with Bruno de Finetti's subjective theory. Worksheets and interactive exercises guide learners to calculate probabilities of various events, reinforcing the understanding of independent and dependent events. This hands-on approach fosters critical thinking and enhances mathematical skills.

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Understanding Probability: Activities for Class II.C Students

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  1. WHAT IS PROBABILITY? CLIL project Class II C

  2. ACTIVITIES CLIL project Class II C

  3. likely probable coin outcome sample space Jack King probability set event Gambing

  4. CLASSICAL DEFINITION FREQUENTIST DEFINITION SUBJECTIVE PROBABILITY Bruno De Finetti proposed the subjective theory of Probability and he worked in Triest in the first half of the XX century (University, Assicurazioni Generali) favourable possible probability divided outcomes favourable cases 3/6 = 1/2 3/10 4/10 12/90 =6/45 2/5 X 0 X 0 X 1 X 0 X 0 X 0 X 1 X 0 X 1 X 1

  5. J A C K A SE TO SS N E P OBABI LI TY F R E Q U N T I T L P L ACE D R A W F V O R A B L E F I NE TT I L K E L Y H E D C R T A I N C O N AR D Z E O

  6. P(blue)=3/9=1/3 P(not blue)= 1 – 1/3=2/3 P(jack)=4/40=1/10 P(not jack)= 1 – 1/10=9/10 P(>75)=15/90=1/6 P(not >75)= 1 – 1/6=5/6 P(odd)=3/6=1/2 P(even: not odd)= 1 – 1/2=1/2 P (your birthday)=1/365 P(not your birthday)= 1 – 1/365=364/365 P(good)=3/8 P(bad: not good)= 1 – 3/8=5/8 P(I complete)=0,23 P(I don’t complete)= 1 – 0,23 = 0,77 P(wins)=0,73 P(loses: doesn’t win)= 1 – 0,73 = 0,27 P(7)=0 P(not 7)= 1 – 0 = 1

  7. x x x x x x x x x 4/52 4/51 dependent P=4/52  4/51=16/2652 4/52 4/52 independent P=4/52  4/52=16/2704 1/37 1/37 independent P=1/37  1/37=1/1369

  8. N T ER SE C T I ON I N D I P E N D E N T M U L I P L I C A T I O N O M U T U L L Y D S JO I T X C L U S I V E A D D T I O N A D V E N N X X X X X X X X

  9. III) Find the probability of the events formed by the following couples of disjoint events: 1/6 1/6 1/6 + 1/6 =2/6 1/4 1/4 1/4 + 1/4 =1/2 1/37 0/37 1/37 + 0/37 =1/37 7/90 9/90 7/90 + 9/90 =16/90 0,45+0,15 =0,60 6/14 5/14 6/14 + 5/14 =11/14

  10. Name and Surname______________________________ • ACTIVITY 6. TOTAL PROBABILITY and REVIEW • Find the probability of the events formed by the following couples of not disjoint events: 13/52 12/52 3/52 13/52+12/52-3/52 7/90 9/90 1/90 7/90+9/90-1/90=15/90 14/25 11/25 6/25 14/25+11/25-6/25=19/25

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