Question

Группа туристов состоит из 12 парней и 8 девушек.Из них выбирают 4 участника для соревнований.Какова вероятность того,что среди выбранных будет два парня и две девушки?

Answer 1

Общее число вариантов 4 из 20       N = 20!/(4! * 16!)
Число благоприятных вариантов 2 из 12 умножить на 2 из 8
M = 12!/(2! * 10!)  *  8!/(2! * 6!)
P = M/N = (4! * 16! * 12! * 8!)/ (20! * 2! * 10! * 2! * 6!)=
= (6*11*12*7*8)/(17*18*19*20) = (4*11*2)/ (17 * 19 * 5)= 88/1615 

Answer 2

Calculation of Probability

To calculate the probability of selecting two boys and two girls from a group of 12 boys and 8 girls, we can use the concept of combinations.

The total number of ways to choose 4 participants from a group of 20 (12 boys + 8 girls) is given by the combination formula:

C(n, r) = n! / (r!(n-r)!)

Where: - n is the total number of participants (20 in this case) - r is the number of participants to be chosen (4 in this case) - ! denotes the factorial operation

In this case, we want to calculate the probability of selecting 2 boys and 2 girls, so we need to calculate the number of ways to choose 2 boys from 12 and 2 girls from 8, and then divide it by the total number of ways to choose 4 participants from 20.

Let's calculate the probability step by step:

1. Calculate the number of ways to choose 2 boys from 12: - C(12, 2) = 12! / (2!(12-2)!) = 66

2. Calculate the number of ways to choose 2 girls from 8: - C(8, 2) = 8! / (2!(8-2)!) = 28

3. Calculate the total number of ways to choose 4 participants from 20: - C(20, 4) = 20! / (4!(20-4)!) = 4845

4. Calculate the probability: - Probability = (Number of favorable outcomes) / (Total number of possible outcomes) - Probability = (66 * 28) / 4845 = 0.381

Therefore, the probability of selecting two boys and two girls from the given group is approximately 0.381 or 38.1%.