Question

В классе мальчиков вдвое больше, чем девочек. Известно, что при случайном выборе двух дежурных вероятность того, что оба выбранных окажутся девочками, равна 10%. Сколько в классе учащихся? А. 15. Б. 18. В. 24. Г. 21.

Answer 1

Двадцать четыре учеников в классе

Answer 2

Problem Analysis

We are given that in a class, the number of boys is twice the number of girls. We also know that when two students are randomly chosen as class monitors, the probability of both being girls is 10%. We need to determine the total number of students in the class.

Solution

Let's assume the number of girls in the class is 'x'. According to the given information, the number of boys is twice the number of girls, so the number of boys is '2x'.

The total number of students in the class is the sum of the number of boys and the number of girls, which is '2x + x = 3x'.

We are also given that the probability of both chosen students being girls is 10%. Since the selection is random, we can assume that the probability of choosing any student as the first monitor is 1. Therefore, the probability of choosing a girl as the first monitor is 'x/3x = 1/3'.

Since the first monitor is not replaced, the probability of choosing a girl as the second monitor, given that the first monitor is a girl, is 'x-1/3x-1 = (x-1)/(3x-3)'.

The probability of both monitors being girls is the product of the probabilities of choosing a girl as the first monitor and choosing a girl as the second monitor, given that the first monitor is a girl. Therefore, we have:

(1/3) * (x-1)/(3x-3) = 10/100

Simplifying the equation:

(x-1)/(3x-3) = 10/100

Cross-multiplying:

100(x-1) = 10(3x-3)

100x - 100 = 30x - 30

70x = 70

x = 1

So, the number of girls in the class is 1, and the number of boys is twice that, which is 2. Therefore, the total number of students in the class is 1 girl + 2 boys = 3 students.

Answer

The correct answer is 3.