Slide 1

CME12, 2012.07.04. Rzeszw, Poland Gergely Wintsche Generalization through problem solving Gergely Wintsche Mathematics Teaching and Didactic Center Faculty of Science Etvs Lornd University, Budapest

Slide 2

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

Slide 3

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

Slide 4

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

Slide 5

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

Slide 6

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

Slide 7

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

Slide 8

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

Slide 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

Slide 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

Slide 11

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

Slide 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

Slide 13

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

Slide 14

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

Slide 15

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

Slide 16

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

Slide 17

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

Slide 18

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

Slide 19

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

Slide 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.

Slide 21

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

Slide 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