Question

Студент из 15 вопросов знает ответы только на 7 вопросов. Определить вероятность того, что из 5 наугад выбранных вопросов он знает ответы на 3 вопроса.

Answer 1

Ответ:

$\frac{3}{5}$

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Answer 2

Problem Statement

A student knows the answers to only 7 out of 15 questions. We need to determine the probability that out of 5 randomly chosen questions, the student knows the answers to 3 of them.

Solution

To solve this problem, we can use the concept of combinations and probability.

The total number of ways to choose 5 questions out of 15 is given by the combination formula:

C(n, r) = n! / (r!(n-r)!)

Where: - n is the total number of questions (15 in this case) - r is the number of questions we want to choose (5 in this case) - ! denotes the factorial operation

So, the total number of ways to choose 5 questions out of 15 is:

C(15, 5) = 15! / (5!(15-5)!) = 3003

Now, let's consider the number of ways the student can choose 3 questions that they know the answers to out of the 7 questions they know. This can be calculated using the combination formula as well:

C(7, 3) = 7! / (3!(7-3)!) = 35

Finally, to calculate the probability, we divide the number of favorable outcomes (choosing 3 questions the student knows out of the 7 they know) by the total number of possible outcomes (choosing 5 questions out of 15):

Probability = C(7, 3) / C(15, 5) = 35 / 3003 ≈ 0.0116

Therefore, the probability that the student knows the answers to 3 out of 5 randomly chosen questions is approximately 0.0116 or 1.16%.