A shuttle bus for a festival stops at the parking lot every 18 minutes and stays at the lot for 2 minutes. If you go to the festival at a random time, what is the probability that the shuttle bus will be at the parking lot when you arrive?
let's assume it is noon and the bus has just arrived.
the bus will be there from 12:00 - 12:02
again from 12:20-12:22
again from 12:40 - 12:42
for a total of 6 minutes in 60 minutes.
prob(of stated event) = 6/60 = 1/10
To find the probability of the shuttle bus being at the parking lot when you arrive, we need to determine the length of a full cycle: the time it takes for the shuttle bus to complete a round trip, including both the time at the parking lot and the time between two consecutive arrivals at the parking lot.
The shuttle bus stops at the parking lot every 18 minutes and stays for 2 minutes, so the total time for one complete cycle is 18 minutes (time between arrivals) + 2 minutes (time at the lot) = 20 minutes.
Now, let's assume that you arrive at a random time. Since the shuttle bus has a full cycle length of 20 minutes, there are 20 possible arrival time slots within each cycle where you could potentially arrive and find the shuttle bus at the parking lot.
Therefore, the probability of the shuttle bus being at the parking lot when you arrive can be calculated as:
Probability = (time spent at the lot) / (length of a full cycle)
= 2 minutes / 20 minutes
= 1/10
= 0.1
= 10%
So, the probability that the shuttle bus will be at the parking lot when you arrive is 10%.
To calculate the probability that the shuttle bus will be at the parking lot when you arrive, we need to determine the time period during which you could potentially arrive and calculate the proportion of that time period when the shuttle bus is at the parking lot.
First, let's consider the time cycle of the shuttle bus:
- The shuttle bus stops at the parking lot every 18 minutes.
- It stays at the lot for 2 minutes before departing again.
This makes a total cycle time of 18 + 2 = 20 minutes.
Now, let's break down this cycle into two parts:
1. The period when the bus is at the parking lot: This is the 2-minute interval when the bus is stationary at the parking lot.
2. The period when the bus is away from the parking lot: This is the 18-minute interval when the bus is on its way to or from the parking lot.
Since the shuttle bus is in a continuous cycle, we can assume that the probability of the shuttle bus being at the parking lot is the same at any given time within the 20-minute cycle.
Now, to calculate the probability that the shuttle bus will be at the parking lot when you arrive, we need to determine the proportion of time you could potentially arrive during the 20-minute cycle.
Since you arrive at a random time, you could arrive at any minute within the 20-minute cycle. Therefore, the proportion of time you could potentially arrive is 1/20.
Finally, the probability that the shuttle bus will be at the parking lot when you arrive is equal to the proportion of time during the cycle that the bus is at the parking lot, which is 2/20 = 1/10.
Therefore, the probability that the shuttle bus will be at the parking lot when you arrive is 1/10 or 0.1.