The probability that a driver stopping at petrol station

  • Thread starter TomJerry
  • Start date
  • Tags
    Probability
In summary, the probability that a driver stopping at a petrol station will have neither his car tyres nor oil checked is 0.658. This is calculated by taking the complement of the probability that either his tyres or oil will be checked, which is found by subtracting the probability of both being checked (0.07) from the sum of the probabilities of each being checked individually (0.012 + 0.29 = 0.302). Therefore, P(A' union B') = 1 - 0.302 = 0.698, and P(A' intersection B') = 0.698 - 0.07 = 0.658.
  • #1
TomJerry
50
0
Question:
The probability that a driver stopping at petrol station will have only his car tyre checked is 0.012, the probability that he will have the oil checked is 0.29 and the probability that he will have both oil and tyre's checked is 0.07. What is the probability that a driver stopping at the station will have neither his car tyres nor oil checked

Solution:

Let A be he checks his tyres
P(A) = 0.012
P(A') = 1 - 0.012

Let B be he checks oil
P(B) = 0.29
P(B') = 1 - 0.29

P(A intersection B) = 0.07

We need to find P(A' union B')

P(A' union B') = P(A') + P(B') - P(A' intersection B')

I m stuck here don't know how to go forward from here
 
Physics news on Phys.org
  • #2
Hi TomJerry! :smile:

Hint: P(A) = P(A and B) + P(A and not-B) :wink:

(or just draw a Venn diagram and measure the area)
 

1. What is the probability of a driver stopping at a petrol station?

The probability of a driver stopping at a petrol station depends on various factors such as the distance traveled, the fuel efficiency of the vehicle, and the availability of other petrol stations along the route. It is difficult to provide a specific probability without considering these factors.

2. How can we calculate the probability of a driver stopping at a petrol station?

To calculate the probability of a driver stopping at a petrol station, we need to consider the total number of petrol stations along the route and the average distance between each stop. We can then use these values to apply the Poisson distribution formula to calculate the probability.

3. Does the time of day affect the probability of a driver stopping at a petrol station?

Yes, the time of day can affect the probability of a driver stopping at a petrol station. For example, during peak travel hours or holidays, the probability may be higher as more people are on the road and need to refuel. On the other hand, during late-night or early morning hours, the probability may be lower as there is less traffic on the road.

4. What other factors can influence the probability of a driver stopping at a petrol station?

Apart from distance traveled and time of day, other factors that can influence the probability of a driver stopping at a petrol station include the price of fuel, the availability of other amenities at the petrol station, and the driver's personal preferences. For example, if the fuel price is significantly higher at one petrol station compared to others, the driver may choose to skip it and wait for a cheaper option.

5. How accurate are the calculations of the probability of a driver stopping at a petrol station?

The accuracy of the calculations depends on the accuracy of the data used and the assumptions made. While it is possible to calculate the probability using the Poisson distribution, it may not always accurately reflect real-world situations as it relies on certain assumptions. Additionally, unexpected events such as road closures or detours can also affect the probability of a driver stopping at a petrol station.

Similar threads

I Are these events independent?
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
1K
I Probability of White Ball in Box of 120 Balls: Solved!
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
I Adding random numbers: Tolerance analysis
    • Set Theory, Logic, Probability, Statistics
Replies
7
Views
308
MHB Poisson Process - Number of cars that a petrol station can service
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
B Conditional Probability, Independence, and Dependence
    • Set Theory, Logic, Probability, Statistics
Replies
10
Views
2K
Device For Driver Communication Between Vehicles
    • General Discussion
Replies
11
Views
907
What are the probabilities for events A and B in a set of 10 cards?
    • Precalculus Mathematics Homework Help
Replies
3
Views
1K
Launch service between two stations along a flowing river
    • Introductory Physics Homework Help
Replies
21
Views
150
Probability Syntax: Types 1, 2 & 3 Defects
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
5K
If duelist A shoots first, what is the probability A wins?
    • Calculus and Beyond Homework Help
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top