# Relearning Probability

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.

Stephen Tashi
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!