Allen and Bethany each arrive at a party at a random time between 1:00 and 2:00. Each stays for 15 minutes, then leaves. What is the probability that Allen and Bethany see each other at the party?
Both need to be there at sometime during the same 15 minutes.
15/60 = .25
To find the probability that Allen and Bethany see each other at the party, we need to determine the time overlap between their stays.
Let's break down the problem step by step:
Step 1: Determine the possible arrival times for both Allen and Bethany.
Since both Allen and Bethany arrive at a random time between 1:00 and 2:00, they have 60 minutes to choose their arrival time.
Step 2: Find the time overlap.
To see each other at the party, Allen and Bethany need to be there at the same time, or their visits need to overlap.
Let's consider Allen's visit. Since Allen stays for 15 minutes, there is a 15-minute window during which Bethany's arrival time could overlap.
Step 3: Calculate the probability of the time overlap.
To calculate the probability, we need to determine the length of the time overlap relative to the total time window.
The total time window is 60 minutes.
Since Allen stays for 15 minutes, there is a 15-minute window for Bethany's arrival to overlap.
Therefore, the probability of the time overlap is 15/60, which simplifies to 1/4.
Hence, the probability that Allen and Bethany see each other at the party is 1/4 or 0.25.