Question

Научная конференция проводится в 4 дня . В его запланировано 60 докладов : в первые два дня - по 12 докладов , остальные распределены поровну между третьим и четвёртый днями. Порядок докладов определяется случайным образом . Какова вероятность что доклад профессора М. окажется запланированным на последний день конференции

Answer 1

1, 2 день - 12 докладов
3,4 - (60-24)/2=18 докладов
вероятность - отношение нужных вариантов ко всем, т.е,
18/60=0,3

Answer 2

Calculation of Probability

To calculate the probability that Professor M.'s presentation will be scheduled on the last day of the conference, we need to consider the total number of possible arrangements and the number of favorable outcomes.

The total number of possible arrangements can be calculated by finding the total number of ways to distribute the presentations among the four days. Since the first two days have 12 presentations each, and the remaining presentations are evenly distributed between the third and fourth days, we have:

Total number of possible arrangements = (number of ways to distribute the first two days) * (number of ways to distribute the remaining presentations on the third and fourth days)

The number of ways to distribute the first two days is the number of ways to choose 12 presentations out of the total 60 presentations, which can be calculated using the combination formula:

Number of ways to distribute the first two days = C(60, 12)

The number of ways to distribute the remaining presentations on the third and fourth days is the number of ways to choose the remaining presentations (60 - 24 = 36) out of the total remaining presentations, which can also be calculated using the combination formula:

Number of ways to distribute the remaining presentations on the third and fourth days = C(36, 24)

The number of favorable outcomes is the number of ways to choose the professor's presentation out of the remaining presentations (36 - 1 = 35), which can be calculated using the combination formula:

Number of favorable outcomes = C(35, 24)

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible arrangements:

Probability = Number of favorable outcomes / Total number of possible arrangements

Let's calculate the probability using the given information.