Question

Студент выучил 20 вопросов из 30. на экзамене ему задают 2 вопроса. какова вероятность того что он сдаст экзамен, если для этого надо ответить хотябы на один вопрос. Очень срочно

Answer 1

Вероятность того, что студент не сдаст. 
Сначала студент должен вытянуть билет, который не выучил. Эта вероятность равна 
$\frac{10}{30} = \frac{1}{3}$.

Потом снова нужно вытянуть билет, который не выучил. Теперь таких билетов осталось 9, а всего билетов 29. Значит, эта вероятность равна

$\frac{9}{29}$

Теперь нужно перемножить эти вероятности

$\frac{1}{3} \frac{9}{29} = \frac{3}{29}$ - получается вероятность несдачи экзамена.

Теперь надо найти противоположную к этой вероятность
$1- \frac{3}{29} = \frac{29-3}{29} = \frac{26}{29}$ - это вероятность сдачи экзамена.

Ответ: $\frac{26}{29}$ - вероятность сдачи экзамена.

Answer 2

Calculation of Probability

To calculate the probability of the student passing the exam by answering at least one question correctly, we need to consider the number of questions the student has studied and the number of questions they will be asked on the exam.

Given that the student has studied 20 out of 30 questions, there are 10 questions that they have not studied. However, they will only be asked 2 questions on the exam.

To calculate the probability, we can use the concept of complementary events. The probability of passing the exam by answering at least one question correctly is equal to 1 minus the probability of failing to answer both questions correctly.

Calculation Steps

1. Calculate the probability of answering both questions incorrectly: - The probability of answering a question incorrectly is equal to the number of questions the student has not studied (10) divided by the total number of questions they could be asked (30). - Therefore, the probability of answering both questions incorrectly is (10/30) * (10/30).

2. Calculate the probability of passing the exam by answering at least one question correctly: - The probability of passing the exam is equal to 1 minus the probability of answering both questions incorrectly. - Therefore, the probability of passing the exam is 1 - [(10/30) * (10/30)].

Calculation Result

The probability of the student passing the exam by answering at least one question correctly is approximately 0.7778 or 77.78%.

Please note that this calculation assumes that the student's performance on each question is independent of each other and that the questions are equally likely to be asked on the exam.