# Relearning Probability: Find the Best Textbook to Pass Exam

• lizzie96'
In summary, this person struggled with probability and needs to relearn it by the summer in order to pass their university year. They recommend a textbook for self-teaching that covers the topics mentioned in this conversation.
lizzie96'
Hi,

I am in my first year at university and I really struggle with even very elementary probability. I can’t visualise anything like I do in my other modules, and I get confused with problems. After completely failing the exam, I now have to resit next summer if I am to be allowed into next year, and the resit will be much harder than the main exam. This means that in order to pass the year, I need to relearn probability thoroughly by the summer and properly understand all the details. Can anyone recommend a textbook for effectively self-teaching? I used Sheldon Ross’ “First course in Probability” first time round but I found it hard to follow and the problems mainly don’t have solutions. I need an introductory textbook at a similar level, with careful and detailed explanations, and plenty of difficult practice problems with answers so I can revise effectively.

Thanks for any help!

I like Elementary probability theory by Kai Chung. You may want to supplement it with chapters from a discrete mathematics book for combinatorics. The other option would be reading a more advanced book to get the intuition, and then coming back to the level of Ross for problems.

lizzie96' said:
This means that in order to pass the year, I need to relearn probability thoroughly by the summer and properly understand all the details. Can anyone recommend a textbook for effectively self-teaching?

USA residents can visualize the typical 1-semester introductory course for probabiliy in a US university. but I think you might be in the UK educational system. If so, you'll get better advice from USA forum members if you say what topics were covered in probability. (For example, how heavily did the course emphasize combinatorics? Did you study random variables?)

These were the topics covered, corresponding to the first 8-9 chapters of Ross.

Counting, foundations of probability, sample spaces and events
Sample spaces with equally likely outcomes
Conditional probability, bayes’ formula
Independence
Discrete random variables, expectation and variance
Bernoulli, binomial, poisson, geometric, negative binomial RVs
Uniform, normal, exponential, gamma RVs
Sums of independent RVs, limit theorems: Markov, Chebyshev, weak law large numbers, moment generating functions
Central limit theorem, poisson process

Probability was hard for me too. We used a book by Hogg and Tanis, which was similar in many ways to Ross, and for me it was horrible. I can't say whether or not the following options will address everything on your exam, but they might be worth checking out just to see if they help you to get a better feel for the subject:

Introduction to Probability by Blitzstein (I haven't used it, but it appears to take a unique approach and is getting good reviews) https://www.amazon.com/dp/1466575573/?tag=pfamazon01-20

Introduction to Probability, Statistics, and Random Processes by Pishro-Nik (again, sorry, I haven't used this personally, but it looks clear and has lots of worked examples) free online access at http://www.probabilitycourse.com/ or relatively cheap hard copy on Amazon.

I hope this helps. Best wishes!

## 1. What is the importance of relearning probability?

Relearning probability is important because it allows you to refresh your knowledge and understanding of the subject, which can help you improve your performance on exams and in real-world applications.

## 2. How do I choose the best textbook for relearning probability?

When choosing a textbook, consider your learning style, the level of detail you need, and the reputation of the author and publisher. It's also helpful to read reviews and ask for recommendations from professors or peers.

## 3. Are there any specific features I should look for in a probability textbook?

Some features to look for include clear explanations, relevant and diverse examples, practice problems, and well-organized content. You may also want to consider if the textbook comes with online resources or interactive tools.

## 4. How often should I relearn probability to be successful?

The frequency of relearning probability depends on the individual and their goals. It's recommended to regularly review material and practice problems, but the exact frequency may vary. It's important to find a schedule that works for you and stick to it.

## 5. Can I use multiple textbooks to relearn probability?

Yes, you can use multiple textbooks to relearn probability. In fact, using different resources can provide a more well-rounded understanding of the subject. Just be sure to stay organized and focused on your learning goals.

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