Question

Из 10 языковедов 4 финно-угроведа.Из них по жребию составляют комиссию в составе 3 человека. Какова вероятность, что среди членов комиссии будет 2 фина?

Answer 1

Общее число вариантов собрать комиссию равно количеству сочетаний из 10 по 3 и составляет С₁₀³=10!/(3!*7!)=120. Благоприятных для нас вариантов всего 36. Пусть финны будут 7, 8, 9 и 10 членами комиссии. Тогда благоприятные варианты 1, 7, 8; 1,7,9; 1, 7, 10; 1,8,9; 1, 8, 10; 1,9,10.Итого 6 вариантов. Также если начать  со 2 члена, с 3-го, 4-го, 5-го и 6-го членов. Теперь вероятность ищем как отношение благоприятного числа событий к общему, то есть P=36/120=0,3.

Answer 2

Problem Analysis

We are given that out of 10 linguists, 4 specialize in Finno-Ugric languages. From these 10 linguists, a commission of 3 members will be formed by drawing lots. We need to find the probability that 2 of the members of the commission will be specialists in Finno-Ugric languages.

Solution

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

Let's calculate the number of favorable outcomes first. We need to choose 2 out of the 4 Finno-Ugric specialists and 1 out of the remaining 6 linguists who are not specialists in Finno-Ugric languages. The number of ways to choose 2 out of 4 is given by the combination formula:

Number of ways to choose 2 out of 4 = C(4, 2) = 4! / (2! * (4-2)!) = 6

Similarly, the number of ways to choose 1 out of 6 is given by:

Number of ways to choose 1 out of 6 = C(6, 1) = 6

Now, let's calculate the total number of possible outcomes. We need to choose 3 out of the 10 linguists. The number of ways to choose 3 out of 10 is given by:

Number of ways to choose 3 out of 10 = C(10, 3) = 10! / (3! * (10-3)!) = 120

Therefore, the number of favorable outcomes is 6 * 6 = 36, and the total number of possible outcomes is 120.

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes = 36 / 120 = 0.3

So, the probability that 2 of the members of the commission will be specialists in Finno-Ugric languages is 0.3.

Answer

The probability that among the members of the commission there will be 2 specialists in Finno-Ugric languages is 0.3.