Question

На первом курсе 70 студентов. Из них 30 человек занимаются физкультурой в секции гимнастики, 20 – в секции лыжного спорта, остальные – легкоатлеты. Вероятность получить зачет «автоматом» у гимнастов – 0,8; у лыжников – 0,85; у легкоатлетов – 0,75. Найти вероятность того, что наудачу выбранный с курса студент получит зачет по физкультуре автоматически.

Answer 1

70-30-20=20
30*0,8+20*0,85+20*0,75=24+17+15=56
56/70=4/5=0,8

Answer 2

Problem Analysis

We are given the following information: - There are 70 students in the first year. - 30 students participate in gymnastics. - 20 students participate in skiing. - The remaining students are athletes. - The probability of automatically passing the physical education exam for gymnasts is 0.8. - The probability of automatically passing the physical education exam for skiers is 0.85. - The probability of automatically passing the physical education exam for athletes is 0.75.

We need to find the probability that a randomly selected student from the course will automatically pass the physical education exam.

Solution

To find the probability, we need to calculate the weighted average of the probabilities for each group of students.

Let's calculate the probability for each group: - The probability for gymnasts is 0.8. - The probability for skiers is 0.85. - The probability for athletes is 0.75.

Now, let's calculate the weighted average: - The number of gymnasts is 30, so the weighted probability for gymnasts is 30 * 0.8 = 24. - The number of skiers is 20, so the weighted probability for skiers is 20 * 0.85 = 17. - The number of athletes is 70 - 30 - 20 = 20, so the weighted probability for athletes is 20 * 0.75 = 15.

Finally, let's calculate the total weighted probability: - The total weighted probability is the sum of the weighted probabilities for each group: 24 + 17 + 15 = 56.

Therefore, the probability that a randomly selected student from the course will automatically pass the physical education exam is 56/70.

Answer

The probability that a randomly selected student from the course will automatically pass the physical education exam is 56/70.