Question

farmer opens shop at a uniform random time between 10am and 11am and stays open for 20 minutes, customer arrives at a uniform random time between 10 and 11 am and stays for 40 minutes before leaving. what is the probability they will meet

Answer 1

On average, two minutes elapse between two successive customer arrivals, and it takes six minutes on average for three customers to arrive. The probability of a customer arriving within one minute is 50%, based on uniform customer arrival times. The probability scenarios provided are based on uniform distribution, which allows for straightforward computation.

Step-by-step explanation:

In order to find the probability that the farmer and the customer will meet, we need to consider their respective time windows of availability. The farmer opens his shop at a uniform random time between 10 am and 11 am and is available for 20 minutes. The customer arrives at a random time within the same hour and stays for 40 minutes. To calculate this probability, we would need to consider all possible overlapping time intervals between the customer's 40-minute stay and the farmer's 20-minute window. However, the question is asking for specific probability calculations related to customer arrival times and not the direct scenario involving the farmer and the customer.

Regarding the additional information provided:

1. Since we expect a new customer every two minutes on average, it means that on average, two minutes elapse between two successive arrivals of customers.
2. For three customers to arrive, at an average of one customer every two minutes, it would take six minutes on average for all three to arrive.
3. The probability that another customer arrives within one minute is calculated by considering the uniform distribution behavior for the arrivals, which is 1 customer per 2 minutes. For a time interval of one minute, the likelihood would be 0.5 or 50% because there is half a chance in the two-minute average arrival window that they will arrive within any given minute.
4. Regarding the given time to wait for a rural bus that is uniformly distributed between 0 to 75 minutes, for 100 sampled riders, statistical analysis would be required based on uniform distribution to determine how long they waited.
5. For a delivery service that operates continuously and uniformly from 10 a.m. to 2 p.m., if it's now past noon, there are two hours remaining in the delivery window. The probability that a person must wait at least another one and a half hours is found by considering the time left and the uniform distribution of delivery times.