Question

На экзамен нужно выучить 50 вопросов, а студент выучил только 43 В билете два вопроса, причём каждый вопрос встречается в билетах ровно 1 раз. Студент наугад тянет один из билетов. Найдите вероятность того, что он будет знать все вопросы в билете, если в каждом билете не более одного невыученного студентом вопроса.

Answer 1

Так как вопросов 50, а в билете 2 вопроса, то билетов всего 25. Ученик знает 43 вопроса, значит 7 вопросов он не знает. В каждом билете ученик не знает не более одного вопроса, значит всего билетов, в которых есть неизвестные вопросы 7 штук, а билетов, в которых все вопросы известны 18 штук. Получается, что искомая вероятность равна 18/25=0,72

Answer 2

чтобы найти вероятность мы делим выученные билеты на  количество вопросов, и у нас получается так
43/50=0,86
ответ: 0,86

Answer 3

Problem Analysis

To find the probability that the student will know all the questions on the ticket, we need to consider the following information: - The student has learned 43 out of 50 questions. - Each ticket contains two questions, and each question appears exactly once on the tickets. - The student randomly selects one ticket.

Solution

Let's break down the problem step by step:

1. Calculate the total number of possible tickets: - Since each ticket contains two questions, and there are 50 questions in total, the number of possible tickets is given by the combination formula: C(50, 2) = 50! / (2! * (50-2)!) = 1225.

2. Calculate the number of tickets that contain at least one question the student hasn't learned: - The student has learned 43 out of 50 questions, so there are 7 questions that the student hasn't learned. - To calculate the number of tickets with at least one unknown question, we can subtract the number of tickets with both known questions from the total number of tickets. - The number of tickets with both known questions is given by the combination formula: C(43, 2) = 43! / (2! * (43-2)!) = 903. - Therefore, the number of tickets with at least one unknown question is 1225 - 903 = 322.

3. Calculate the number of tickets that contain only known questions: - Since each ticket contains two questions, and the student has learned 43 questions, the number of tickets with only known questions is given by the combination formula: C(43, 2) = 903.

4. Calculate the probability that the student will know all the questions on the ticket: - The probability is given by the number of favorable outcomes (tickets with only known questions) divided by the total number of possible outcomes (total number of tickets). - Therefore, the probability is 903 / 1225 ≈ 0.737959.

Answer

The probability that the student will know all the questions on the ticket is approximately 0.737959.

Explanation

To solve this problem, we first calculated the total number of possible tickets, which is 1225. Then, we calculated the number of tickets that contain at least one question the student hasn't learned, which is 322. Subtracting this from the total number of tickets gives us the number of tickets with only known questions, which is 903. Finally, we divided the number of tickets with only known questions by the total number of tickets to find the probability, which is approximately 0.737959.