Question

На конференцию прибыли 4 учёных из Франции 2 из Болгарии 2 из Германии. Каждый на конференции делает один доклад. Порядок докладов определяется жеребьевкой. Найдите вероятность того что восьмым окажется доклад учёного из Франции

Answer 1

4+2+2=8 ученых всего
$\frac{4}{8} =0,5$ - вероятность того, что восьмым окажется доклад ученого из Франции
Ответ:0.5

Answer 2

Problem Analysis

We have a total of 4 scientists from France, 2 from Bulgaria, and 2 from Germany attending a conference. Each scientist will give one presentation, and the order of the presentations will be determined by a lottery. We need to find the probability that the eighth presentation will be given by a scientist from France.

Solution

To find the probability, we need to calculate the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes can be calculated using the formula for permutations. Since there are 8 scientists in total, the total number of possible outcomes is 8!.

The number of favorable outcomes is the number of ways the eighth presentation can be given by a scientist from France. Since there are 4 scientists from France, the number of favorable outcomes is 4!.

Therefore, the probability can be calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Let's calculate the probability.

Calculation

The total number of possible outcomes is 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.

The number of favorable outcomes is 4! = 4 x 3 x 2 x 1 = 24.

Therefore, the probability that the eighth presentation will be given by a scientist from France is 24/40,320, which simplifies to 1/1,680.

Answer

The probability that the eighth presentation will be given by a scientist from France is 1/1,680.