Question

В классе 9 мальчиков и 16 девочек. Среди учащихся класса случайным образом выбирают двоих дежурных. Найдите вероятность того,что дежурить будут две девочки!

Answer 1

25!:(2!*23!)=300
16!:(2!*14!)=120
120:300=0,4
0,4*100=40%

Вероятность того что будут дежурить 2 девочки равна 40%

Answer 2

Problem Analysis

In a class of 9 boys and 16 girls, two students are randomly chosen to be on duty. We need to find the probability that both students chosen for duty are girls.

Solution

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

The total number of possible outcomes is the number of ways we can choose any two students from the class, which can be calculated using the combination formula:

Total number of possible outcomes = C(n, k) = n! / (k!(n-k)!)

Where n is the total number of students in the class (25) and k is the number of students chosen for duty (2).

Total number of possible outcomes = C(25, 2) = 25! / (2!(25-2)!) = 25! / (2!23!) = (25 * 24) / (2 * 1) = 300

Now, we need to determine the number of favorable outcomes, which is the number of ways we can choose two girls from the class. Since there are 16 girls in the class, we can calculate this using the combination formula:

Number of favorable outcomes = C(n, k) = n! / (k!(n-k)!)

Where n is the total number of girls in the class (16) and k is the number of girls chosen for duty (2).

Number of favorable outcomes = C(16, 2) = 16! / (2!(16-2)!) = 16! / (2!14!) = (16 * 15) / (2 * 1) = 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

Probability = 120 / 300 = 2/5

Therefore, the probability that both students chosen for duty will be girls is 2/5.