Question

В деканат поступили контрольные работы студентов трех групп в количестве: 30 работ студентов первой группы, 33 работы студентов второй группы, 35 работ студентов третьей группы. Вероятность того, что контрольная работа, написанная студентом первой, второй и третьей групп имеет положительную оценку, равна, соответственно, 0,8, 0,9, 0,7. Какова вероятность того, что взятая наугад контрольная работа имеет положительную оценку?

Answer 1

Перемножь все вероятности
0, 8×0, 9×0, 7=0, 504

Answer 2

Problem Analysis

We are given the number of control works submitted by three groups of students: 30 from the first group, 33 from the second group, and 35 from the third group. We are also given the probabilities of each group's work receiving a positive evaluation: 0.8 for the first group, 0.9 for the second group, and 0.7 for the third group. We need to find the probability that a randomly selected control work has a positive evaluation.

Solution

To find the probability that a randomly selected control work has a positive evaluation, we need to consider the number of control works in each group and the probability of each group's work receiving a positive evaluation.

Let's calculate the total number of control works: - First group: 30 works - Second group: 33 works - Third group: 35 works

The total number of control works is 30 + 33 + 35 = 98.

Now, let's calculate the weighted sum of the probabilities of positive evaluations for each group: - First group: 0.8 * 30 = 24 - Second group: 0.9 * 33 = 29.7 - Third group: 0.7 * 35 = 24.5

The total weighted sum is 24 + 29.7 + 24.5 = 78.2.

Finally, we can calculate the probability that a randomly selected control work has a positive evaluation by dividing the total weighted sum by the total number of control works: Probability = Total weighted sum / Total number of control works = 78.2 / 98 = 0.7969 (rounded to four decimal places).

Therefore, the probability that a randomly selected control work has a positive evaluation is approximately 0.7969.

Conclusion

The probability that a randomly selected control work has a positive evaluation is approximately 0.7969.