I was so close to getting through the unit Probability and Combinatorics this week but fell just short. I’m happy with the effort I put in having watched 38 of the 41 videos and working through all the questions ahead of time before watching how each question was solved. ‘m also happy with what I was able to remember from both probability and combinatorics. I was able to come up with the correct answer for every question before watching how they were solved except for the last video I watched on combinatorics. I’m glad that the majority of what I learned in these subjects a few months ago has stuck with me. I’ve said this many times, but it’s interesting/weird how every subject in math seems to make so much more sense when I come back to it after spending time on other subjects. 🤔 🤷🏻‍♂️

The unit started off going through the definition/formula for probability:

Reviewing probability I now realize how fundamental and crucial this formula is and how it’s helpful to think of every probability question this way to simplify them in my head. I also realized how useful it can be to think through probability questions using a probability tree:

After a brief review of probability, I then reviewed Venn Diagrams:

Key things to remember about a Venn Diagram is that the rectangle (a.k.a. the “universe” which is a really weird word to use in my opinion) represents all possible outcomes and each circle represents a specific dataset within all the data that’s being considered. When circles overlap it indicates that two datasets share a common factor that’s also being considered. When adding two circles that overlap you must subtract the value where they overlap from the sum of both circles otherwise you’d be counting that value where they overlap twice. The size of the overlapping section relative to the universe is (the overlapping section/circle A) * (the overlapping section/circle B).

Next, I reviewed the definitions of Independent vs Dependent:

My explanation in the photo is a bit confusing. Simply put, if events are independent from each other, the first event’s outcome doesn’t affect the probability of the second event. The opposite is true for dependent events.

The remainder of my week was spent working through combinatorics questions. Between probability and combinatorics, I’ve always found combinatorics to be the more difficult subject to wrap my head around which was the case this week, as well. That said, the formulas for permutations (n!/(n – k)!) and combinations (n!/(k! * (n – k)!)) both made a lot more sense to me this time around and actually seemed fairly straightforward. (WOO!!)

Here’s an example question from my notes of how to come up with the formula for combinations:

At the end of the week I went through a few videos where Sal combined probability with combinatorics. I was a bit confused working through these questions but understood the general concept of how to do them. I feel like I’m about ~85% of the way to fully wrapping my head around all of permutations, combinations, and probability and am confident I will have it all figured out soon.

Being that I only have 3 videos left to watch in Probability and Combinatorics (800/800 M.P.), I’m sure I’ll get to the course challenge early in the week. I feel pretty good about my understanding of everything I’ve worked through in Precalculus so I’m hoping it won’t take me too many attempts to get a decent score on the challenge so I can FINALLY move on to calculus. I’m getting super tired of writing at the end of each blog post that “I’m just about to get started with calculus” so I will NOT be happy if I have to write it again next week. 😠