Question

при подготовке танца исполнители делятся на три группы по 11 человек. найдите вероятность того, что две подруги света и зина попадут в одну группу.​

Answer 1

Відповідь:

$\frac{1}{9}$

Покрокове пояснення:

Ймовірність того, що Світлана потрапить в першу групу = $\frac{1}{3}$

Ймовірність того, що Зіна потрапить в першу групу = $\frac{1}{3}$

Ймовірність того, що і Світлана і Зіна потраплять в першу групу = $\frac{1}{3} * \frac{1}{3}$

$\frac{1}{3} * \frac{1}{3} = \frac{1}{9}$

Answer 2

Calculating the Probability of Two Friends Being in the Same Group

To calculate the probability of two specific individuals, Sveta and Zina, being in the same group out of three groups of 11 people each, we can use the following approach:

1. Total Number of Ways to Select 2 People from 33: - The total number of ways to select 2 people from 33 (3 groups of 11 people each) is given by the combination formula: - C(n, r) = n! / (r! * (n-r)!), where n is the total number of items, and r is the number of items to choose.

2. Number of Ways to Select Sveta and Zina in the Same Group: - Since Sveta and Zina need to be in the same group, we can consider them as a pair and calculate the number of ways to select the remaining 9 people from the same group. - This can be calculated using the combination formula as well.

3. Calculating the Probability: - Once we have the total number of ways to select 2 people from 33 and the number of ways to select Sveta and Zina in the same group, we can calculate the probability by dividing the latter by the former.

Calculation

The probability of Sveta and Zina being in the same group can be calculated as follows:

1. Total Number of Ways to Select 2 People from 33: - Using the combination formula, we get: - C(33, 2) = 33! / (2! * (33-2)!)

2. Number of Ways to Select Sveta and Zina in the Same Group: - Considering Sveta and Zina as a pair, and selecting 9 more people from the same group, we get: - C(11, 2) * C(11-2, 9)

3. Calculating the Probability: - The probability is given by: - (Number of ways to select Sveta and Zina in the same group) / (Total number of ways to select 2 people from 33)

Let's calculate the probability using the above approach.