Question

Помогите решить задачу с полным объяснением, пожалуйста! Три экзаменатора принимают экзамен по некоторому предмету у группы в 30 человек, причем первый опрашивает 6 студентов, второй - 3 студентов, а третий - 21 студента ( выбор студентов производится случайным образом из списка). Отношение трех экзаменаторов к слабо подготовившимся различное: шансы таких студентов сдать экзамен у первого преподавателя равны 40%, у второго - только 10%, у третьего - 70%. Найти вероятность того, что слабо подготовившийся студент сдаст экзамен.

Answer 1

Можно взять взвешенное среднее:
(6*40%+3*10%+21*70%)/30 = 58%
так что - скорее всего прокатит

Answer 2

Task Explanation and Approach

We are given that three examiners are conducting an exam for a group of 30 students. The first examiner interviews 6 students, the second interviews 3, and the third interviews 21. The probability of a poorly prepared student passing the exam is 40% for the first examiner, 10% for the second, and 70% for the third. We need to find the probability of a poorly prepared student passing the exam.

To solve this problem, we can calculate the overall probability of a poorly prepared student passing the exam by considering the probabilities for each examiner and the number of students they interview.

Calculation

Let's calculate the probability of a poorly prepared student passing the exam.

The probability of a poorly prepared student passing the exam with the first examiner is 40%. The probability of a poorly prepared student passing the exam with the second examiner is 10%. The probability of a poorly prepared student passing the exam with the third examiner is 70%.

We can calculate the overall probability using the following formula: \[ P = \frac{P_1 \cdot n_1 + P_2 \cdot n_2 + P_3 \cdot n_3}{N} \] Where: - \( P_1, P_2, P_3 \) are the probabilities of passing the exam for the first, second, and third examiners respectively. - \( n_1, n_2, n_3 \) are the number of students interviewed by the first, second, and third examiners respectively. - \( N \) is the total number of students.

Let's substitute the given values and calculate the overall probability.

\[ P = \frac{0.40 \cdot 6 + 0.10 \cdot 3 + 0.70 \cdot 21}{30} \]

\[ P = \frac{2.4 + 0.3 + 14.7}{30} \]

\[ P = \frac{17.4}{30} \]

\[ P \approx 0.58 \]

Answer

The probability of a poorly prepared student passing the exam is approximately 58%.