Question

Экзаменационный билет содержит 3 вопроса. Вероятность того что студент ответин на первый и второй вопросы билета, равна 0,9 на третий 0,8. Найдите вероятность того что студент сдаст экзамен, если для этого необходимо ответить хоть на 2 вопроса.

Answer 1

Вероятность
(0.9*2+0.8)/3=86%

Answer 2

Problem Analysis

We are given that an exam ticket contains 3 questions. The probability that a student answers the first and second questions correctly is 0.9, and the probability that they answer the third question correctly is 0.8. We need to find the probability that the student passes the exam by answering at least 2 questions correctly.

Solution

To find the probability that the student passes the exam by answering at least 2 questions correctly, we can calculate the probability of three different scenarios: 1. The student answers all three questions correctly. 2. The student answers the first two questions correctly and the third question incorrectly. 3. The student answers the first question correctly and the second and third questions incorrectly.

We can then add up these probabilities to get the total probability of passing the exam.

Scenario 1: Answering all three questions correctly

The probability of the student answering all three questions correctly is the product of the probabilities of answering each question correctly: - Probability of answering the first question correctly: 0.9 - Probability of answering the second question correctly: 0.9 - Probability of answering the third question correctly: 0.8

Therefore, the probability of answering all three questions correctly is: 0.9 * 0.9 * 0.8 = 0.648.

Scenario 2: Answering the first two questions correctly and the third question incorrectly

The probability of the student answering the first two questions correctly and the third question incorrectly is the product of the probabilities of answering each question correctly or incorrectly: - Probability of answering the first question correctly: 0.9 - Probability of answering the second question correctly: 0.9 - Probability of answering the third question incorrectly: 1 - 0.8 = 0.2

Therefore, the probability of answering the first two questions correctly and the third question incorrectly is: 0.9 * 0.9 * 0.2 = 0.162.

Scenario 3: Answering the first question correctly and the second and third questions incorrectly

The probability of the student answering the first question correctly and the second and third questions incorrectly is the product of the probabilities of answering each question correctly or incorrectly: - Probability of answering the first question correctly: 0.9 - Probability of answering the second question incorrectly: 1 - 0.9 = 0.1 - Probability of answering the third question incorrectly: 1 - 0.8 = 0.2

Therefore, the probability of answering the first question correctly and the second and third questions incorrectly is: 0.9 * 0.1 * 0.2 = 0.018.

Total Probability of Passing the Exam

To find the total probability of passing the exam, we add up the probabilities from all three scenarios: - Probability of answering all three questions correctly: 0.648 - Probability of answering the first two questions correctly and the third question incorrectly: 0.162 - Probability of answering the first question correctly and the second and third questions incorrectly: 0.018

Therefore, the total probability of passing the exam by answering at least 2 questions correctly is: 0.648 + 0.162 + 0.018 = 0.828.

Answer

The probability that the student will pass the exam by answering at least 2 questions correctly is 0.828.