1. CME12, 2012.07.04. – Rzeszów, Poland Gergely Wintsche Generalization through problem solving Gergely Wintsche Mathematics Teaching and Didactic Center Faculty of Science Eötvös Loránd University, Budapest

2. Gergely Wintsche Outline 1. Back to the future 2. Experiments 3. Head runs 4. Ordering the probabilities Part III / 2 – Probability, experiments, statistic

3. Gergely WintschePart III / 3 – Probability, experiments, statistic Back to the future Tomatoes

4. Gergely WintschePart III / 4 – Probability, experiments, statistic Inheritance Tomatoes

5. Gergely WintschePart III / 5 – Probability, experiments, statistic Experiments Die

6. Gergely WintschePart III / 6 – Probability, experiments, statistic Experiments Die

7. Gergely WintschePart III / 7 – Probability, experiments, statistic Head runs Head or Tails Click here to play movie

8. Gergely WintschePart III / 8 – Probability, experiments, statistic Head runs Exactly k long head run 0123 n long series 111 2121 31421

9. Gergely WintschePart III / 9 – Probability, experiments, statistic Head runs Exactly k long head run 0123456… n long series 111 2121 31421 417521 511211521 61202312521 …

10. Gergely WintschePart III / 10 – Probability, experiments, statistic Head runs Head run Exactly k long head run 0123456… n long series 01 112 2134 31578 418131516 511324293132 61214456616364 …

11. Gergely WintschePart III / 11 – Probability, experiments, statistic Head runs

12. Gergely WintschePart III / 12 – Probability, experiments, statistic Head runs Exactly k long head run 0123456… n long series 01 112 2134 31578 418131516 511324293132 61214456616364 …

13. Gergely WintschePart III / 13 – Probability, experiments, statistic Head runs n012345678… A n (3)1248152956108208

14. Gergely WintschePart III / 14 – Probability, experiments, statistic Head runs Heads or tails THTTTHTTHH DDSSDDSDS

15. Gergely WintschePart III / 15 – Probability, experiments, statistic Head runs Head or tails / average

16. Gergely WintschePart III / 16 – Probability, experiments, statistic Head runs Which dice is better

17. Gergely WintschePart III / 17 – Probability, experiments, statistic Head runs Which series are better

18. Gergely WintschePart III / 18 – Probability, experiments, statistic Head runs Which series are better START HT HT 1/2

19. Gergely WintschePart III / 19 – Probability, experiments, statistic Head runs Which series are better

20. Gergely WintschePart III / 20 – Probability, experiments, statistic Head runs Which series are better START HT H T HH HTT HHT P1P1 P2P2 P3P3 P4P4 P i denotes that Andrew is here and win.

21. Gergely WintschePart III / 21 – Probability, experiments, statistic Head runs Which series are better

22. Gergely WintschePart III / 22 – Probability, experiments, statistic Head runs Which series are better START 7 12 29/36 1/36 6/36 29/36 12 7 1/36 6/36