Question

Студент выучил к экзамену 20 из 40 вопросов программы.Найдите вероятность события А: студент знает ответы на два вопроса,предложенные ему экзаменатором?

Answer 1

Итак, у нас всего $C^2_{40}$ вопросов, которые могут спросить у студента.

 

Из них, всего $C^2_{20}$ студент знает.

 

$p = \frac{m}{n} = \frac{C^2_{20}}{C^2_{40}} = \frac{\frac{20!}{18!*2!}}{\frac{40!}{38!*2!}} = \frac{20!*38!*2!}{40!*18!*2!} = \frac{19*20}{39*40} = \frac{19}{39*2} = \frac{19}{78}$

Answer 2

Вероятность рассчитывается по формуле p=n/N ,  где n-число благоприятных исходов,а N общее число событий.

Поэтому в нашем случае p=20/40=0.5

Answer 3

Calculation of Probability

To find the probability of event A, which is the student knowing the answers to two questions proposed by the examiner, we need to know the total number of questions in the exam and the number of questions the student has studied.

Given that the student has studied 20 out of 40 questions, we can calculate the probability as follows:

Probability of event A = (Number of questions studied / Total number of questions) * (Number of questions proposed by the examiner / Number of questions studied)

Let's substitute the values into the formula:

Probability of event A = (20 / 40) * (2 / 20)

Simplifying the expression:

Probability of event A = 0.5 * 0.1

Probability of event A = 0.05

Therefore, the probability of the student knowing the answers to the two questions proposed by the examiner is 0.05.

Please note that the above calculation assumes that the questions proposed by the examiner are randomly selected from the pool of questions the student has studied.