Respuesta :
Answer:
To calculate the theoretical probability that you and your friend will be at the park at the same time for at least a minute, let's break down the time intervals.
Each of you arrives between 1:00 p.m. and 2:00 p.m. and stays for 15 minutes.
Let's denote the time of your arrival as X and the time of your friend's arrival as Y, both uniformly distributed between 1:00 p.m. and 2:00 p.m.
For the two of you to be at the park at the same time for at least a minute, your arrival times must overlap by at least a minute.
Let's define:
- A = Your arrival time
- B = Your friend's arrival time
To find the probability that you both are at the park for at least a minute, we need to find the area of overlap between the two arrival time intervals.
First, let's find the probability that the absolute difference between your arrival time and your friend's arrival time is less than or equal to 15 minutes (the duration you stay at the park).
The probability that your friend arrives within 15 minutes before or after you is 30 minutes out of the total 60-minute interval.
So, the probability that you and your friend will be at the park at the same time for at least a minute is 30/60 = 1/2.
So, the theoretical probability that you and your friend will be at the park at the same time for at least a minute is 1/2.
