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

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

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

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

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

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

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

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

Gergely WintschePart III / 9 – Probability, experiments, statistic Head runs Exactly k long head run … n long series …

Gergely WintschePart III / 10 – Probability, experiments, statistic Head runs Head run Exactly k long head run … n long series …

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

Gergely WintschePart III / 12 – Probability, experiments, statistic Head runs Exactly k long head run … n long series …

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

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

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

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

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

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

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

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.

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

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