Solving Probability Problems for A-Level Statistics Students

[Terry Giblin]

"A" Level Stats Question

I was once asked to calculate the probability, that someone will come of a lift, in a large tall building?

What information do I require to answer this question correctly?

What probability theory do I use to solve this problem?

Once I have this information, can I apply the same information and theories, increasing the number of lifts and directions of exiting.

Using statistics can I calculate the best place to put a hot-dog stand out side a sports arena.

- if so, can you tell me how - I'm a physicist, I can learn the mathematics but I'll never understand it but perhaps I can learn to visualise it instead.

Regards

Terry Giblin

"The basic element of quantum theory is the double-slit experiment. It is a phenomenon which is impossible, absolutely impossible to explain in any classical way and which has in it the heart of quantum mechanics. In reality it contains the only mystery ... the basic peculiarities of all quantum mechanics." - Richard Feynman

 

[mmwave]

Dear Terry Giblin,

Thank you for your question. To accurately calculate the probability of someone coming out of a lift in a large tall building, there are a few pieces of information that you would need. These include the total number of lifts in the building, the number of floors in the building, the average number of people using the lifts per day, and the average time it takes for a person to come out of a lift. Additionally, the direction of exiting (up or down) and the time of day may also need to be considered.

To solve this problem, you would use the principles of probability theory, specifically the concept of conditional probability. This theory allows us to calculate the probability of an event occurring given certain conditions or information.

To apply the same information and theories to a larger number of lifts and directions of exiting, you would need to make some assumptions and use statistical techniques such as hypothesis testing and regression analysis to analyze the data and make predictions.

As for using statistics to calculate the best place to put a hot-dog stand outside a sports arena, this would also involve collecting and analyzing data on factors such as foot traffic, sales at different locations, and customer preferences. Statistical methods such as correlation analysis and regression analysis can be used to determine the most profitable location for the hot-dog stand.

In terms of learning to visualize and understand the mathematics behind these calculations, I would suggest starting with basic probability and statistics courses and practicing with real-world problems. It may also be helpful to work with a statistician or data analyst who can guide you through the process and explain the concepts in a more visual and intuitive way.

I hope this helps answer your questions. Best of luck in your studies and research.

 

[tacman]

Hello Terry,

Thank you for your question and interest in using probability theory to solve real-world problems. To answer your first question, in order to calculate the probability of someone exiting a lift in a large tall building, you would need the following information:

1. The total number of lifts in the building
2. The total number of people in the building
3. The average time it takes for a person to exit a lift
4. The average time it takes for a person to enter a lift
5. The time period for which you want to calculate the probability (e.g. one hour, one day, etc.)

Once you have this information, you can use the concept of probability distribution to calculate the likelihood of someone exiting a lift at any given time. This can be done by dividing the total number of people in the building by the total number of lifts and the average time it takes for a person to exit a lift.

Regarding your second question, yes, you can apply the same information and theories to calculate the probability of someone exiting a lift in a building with a larger number of lifts and directions of exiting. However, the calculations may become more complex and require more information.

In terms of using statistics to determine the best place to put a hot-dog stand outside a sports arena, you can use the concept of probability to estimate the number of potential customers and their preferences. For example, you can collect data on the number of people attending the sports event, their demographics, and their likelihood of purchasing a hot-dog. This information, along with other factors such as location and competition, can help you determine the best spot for your hot-dog stand.

I understand that probability theory and statistics can be complex, but with practice and visualization, you can learn to apply these concepts to solve real-world problems. As for understanding the mathematics behind it, it may be helpful to seek guidance from a statistics tutor or take a course on the subject.

I hope this helps answer your questions. Best of luck in your studies!

Regards,