Question

Автобусы с автостанции уходят строго по расписанию каждые 30 мин. первый автобус уходит в 6 часов последний в 22 часа Гражданка Иванова приходит на автостанцию в случайный момент времени между 12 час. 40 мин и ждёт ближайшего автобуса. какова вероятность того, что Ивановой придётся ждать более 25 минут?

Answer 1

Ей не придётся ждать больше 20 минут

Answer 2

Calculation of Probability

To calculate the probability of Ivanova having to wait for more than 25 minutes, we need to consider the time interval during which she arrives at the bus station and the bus departure schedule.

According to the given information, the buses depart from the bus station every 30 minutes, starting from 6:00 and ending at 22:00. Ivanova arrives at a random time between 12:40 and the next bus departure time.

Let's break down the problem into smaller steps:

Step 1: Calculate the number of buses that depart between 12:40 and 22:00. - The time interval between 12:40 and 22:00 is 9 hours and 20 minutes. - Since the buses depart every 30 minutes, there are 18 buses that depart during this time period.

Step 2: Calculate the probability of Ivanova arriving just before a bus departure. - Since Ivanova arrives at a random time between 12:40 and the next bus departure time, there is an equal chance of her arriving just before or just after a bus departure. - Therefore, the probability of Ivanova arriving just before a bus departure is 1/2.

Step 3: Calculate the probability of Ivanova having to wait for more than 25 minutes. - If Ivanova arrives just before a bus departure, she would have to wait for the entire 30-minute interval until the next bus arrives. - However, if Ivanova arrives just after a bus departure, she would only have to wait for the remaining time until the next bus departure. - The remaining time until the next bus departure is 30 minutes minus the time Ivanova arrives after the previous bus departure. - Since Ivanova arrives at a random time, the average waiting time in this case would be 15 minutes. - Therefore, the probability of Ivanova having to wait for more than 25 minutes is the sum of the probabilities of her arriving just before a bus departure (1/2) and her arriving just after a bus departure and waiting for more than 15 minutes (1/2 * 15/30). - Simplifying this, the probability is 1/2 + 1/4 = 3/4.

So, the probability of Ivanova having to wait for more than 25 minutes is 3/4.