57.0k views
1 vote
my friend and i are hoping to meet for lunch. we will each arrive at our favorite restaurant at a random time between noon and 1 p.m., stay for 15 minutes, then leave. what is the probability that we will meet each other while at the restaurant?

1 Answer

6 votes

To determine the probability of you and your friend meeting each other at the restaurant, we need to consider the range of arrival times and calculate the overlapping time intervals.

Given:

- You and your friend arrive at the restaurant at a random time between noon and 1 p.m.

- You both stay for 15 minutes.

To simplify the calculation, let's consider time in minutes, with 0 representing noon and 60 representing 1 p.m.

The possible arrival time for each of you is randomly distributed within this 60-minute range.

To calculate the probability of meeting, we need to determine the overlapping time intervals when both of you are present at the restaurant. There are two scenarios:

1. Your friend arrives during your 15-minute stay:

In this case, your friend can arrive at any time between (your arrival time - 15 minutes) and (your arrival time + 15 minutes). This results in a 30-minute window during which your friend can arrive and meet you.

2. You arrive during your friend's 15-minute stay:

Similarly, you can arrive at any time between (your friend's arrival time - 15 minutes) and (your friend's arrival time + 15 minutes), resulting in another 30-minute window of overlap.

To calculate the total probability of meeting, we need to sum the probabilities of both scenarios:

Probability = Probability of scenario 1 + Probability of scenario 2

Since both scenarios have the same probability, the final probability can be calculated as:

Probability = 2 * Probability of scenario 1

The probability of scenario 1 can be calculated by dividing the 30-minute window by the total time range of 60 minutes:

Probability of scenario 1 = 30 minutes / 60 minutes = 0.5

Therefore, the total probability of meeting each other at the restaurant is:

Probability = 2 * Probability of scenario 1 = 2 * 0.5 = 1

Hence, the probability of you and your friend meeting each other at the restaurant is 1, or 100%.

User Marvin Klein
by
8.4k points

No related questions found