Question

Студент знает 20 из 30 вопросов какова вероятность что он ответит на 2 вопроса из 3.Решение с пояснениями

Answer 1

Вероятность того,что он ответит на 1 вопрос равна 20/30=2/3.
Вероятность того, что он будет знать ответ на 2 вопрос, если на 1 вопрос он уже 

Answer 2

Problem Analysis

A student knows 20 out of 30 questions and we need to find the probability that they will answer 2 out of 3 questions correctly. To solve this problem, we can use the concept of combinations and probability.

Solution

To find the probability, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

The number of favorable outcomes is the number of ways the student can answer 2 out of 3 questions correctly. This can be calculated using combinations.

The total number of possible outcomes is the total number of ways the student can answer any 2 questions out of the 30 questions they know.

Let's calculate the probability step by step:

Step 1: Calculate the number of favorable outcomes. The student needs to answer 2 out of 3 questions correctly. Since the student knows 20 out of 30 questions, they have 20 questions to choose from. We can calculate the number of ways to choose 2 questions out of 20 using combinations.

Number of favorable outcomes = C(20, 2)

Step 2: Calculate the total number of possible outcomes. The student can choose any 2 questions out of the 30 questions they know. We can calculate the number of ways to choose 2 questions out of 30 using combinations.

Total number of possible outcomes = C(30, 2)

Step 3: Calculate the probability. The probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes

Let's calculate the probability using the given information:

Number of favorable outcomes = C(20, 2) = 20! / (2! * (20-2)!) = 190

Total number of possible outcomes = C(30, 2) = 30! / (2! * (30-2)!) = 435

Probability = 190 / 435 ≈ 0.4368

Therefore, the probability that the student will answer 2 out of 3 questions correctly is approximately 0.4368.

Conclusion

The probability that a student who knows 20 out of 30 questions will answer 2 out of 3 questions correctly is approximately 0.4368.