Задания эвристической олимпиады, блок «Моделирование» , 9-11 классы

Блок «Моделирование»задания к городской эвристической олимпиаде на иностранном языке – 2016

9-11 forms_____________________________________________________________________________

Can you solve the frog riddle?

Let’s Begin

While going through the forest you found a mushroom and decided to eat it. The mushroom turned out to be poisonous. But fortunately, you know that the antidote for this poison is produced by females of a certain species of frogs. Unfortunately, males and females look totally identical. But you know that males have a distinctive croak (sound). You found a frog sitting in front of you. Suddenly you heard a croak behind and then looking aback you saw two other frogs. Which way would you prefer to go? Why?

R ules

1. Only female frogs produce an antidote (cure)

2. Only male frogs have a distinctive croak (sound).

3. You may lick both frogs, sitting behind you, at once.

4. You may make a choice only once.

Walkthrough

Write down, which way you’d prefer to go. Explain your choice.

Sample answers

9-11 form

The direction where two frogs are sitting (on the left) is more preferable. As the result of our choice is random, the task is solved by principles of statistics and the theory of probability. We may come to the conclusion that the probability of finding the female frog on the right is 1 to 2 (50%). But the probability of finding the female frog on the left is higher. The answers 50 and 75% in the ‘left’ situation are wrong. Since we have heard the croak, we definitely know that at least one frog sitting to the left of us is male. Thus, we may arrange the following table:

The last variant is impossible as we heard the croak. As we are allowed to lick both frogs at a time, the first variant comes to death and is irrelevant. But two other variants are quite appropriate. According to the table, the probability of finding the female frog on the left way is 2\3 (67%). And that proves our hypothesis, that the left way is more preferable.

Video, solution and extra materials are here: https://ed.ted.com/lessons/can-you-solve-the-frog-riddle-derek-abbott

Критерии оценивания задания

Адрес публикации: https://www.prodlenka.org/metodicheskie-razrabotki/299160-zadanija-jevristicheskoj-olimpiady-blok-model