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Showing posts from August, 2019

The Monty Hall Problem Solved, Once and For All

The first time I ever encountered the infamous Monty Hall Problem was 5 years ago on a video from one of my favorite YouTubers, Numberphile. The problem states:

"Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to switch your choice?"

The answer is a resounding yes, you are twice as likely to win by switching. However, the problem is seemingly paradoxical and to this day baffles many people - why does switching doors matter in the grand scheme? Through hundreds of YouTube comments on the original videos, I see 2 major misconceptions that I will layout and explain the best that I can.  Misconception 1: The event of the door not opened/picked is independent of the door the host p…

A Wrap to Summer 2019!!!

Summer 2019 was an almost perfect mixture of lying around doing nothing, hanging out with old friends, and self-growth. 
I wanted to use this blog post to reflect on some of the activities I indulged myself in and restrained myself from. I also wanted to use it to peep into the rapidly upcoming future and create some loose goals for myself. 
Reflections TV Shows of the Summer  1. Friends - A casual tv show with characters living various real life possibilities and discussing them in a coffee shop. I loved watching every minute of Friends because of the dynamic and vivacious characters that the storyline had. Every character had a part to play and all of them grew as people in their own way. This show made me love New York even more than I already loved it before. 9.5/10 2. That 70's Show - Another casual tv show centered around a gang of high school reefers that had a cast full of unique characters. I started watching this show since a friend recommended it and it showed up every…

Class Review: Discrete Math and Probability Theory (CS70)

CS70 at UC Berkeley during Summer 2019 was the hardest class I've ever taken. It takes centuries of development in Discrete Mathematics and Probability Theory (some theories took decades to prove or refine) and shoves abstract concepts down your throat in a span of 8 weeks.
I believe that there is no other class at Berkeley in which the disparity between the ability of the students in the course is so stark - students range from International Math Olympiad medalists who have years of rigorous contest math experience to beginning computer science students who hate math and just want to declare the major (a pity that this course is required for that purpose). I fall somewhere in the middle, a math-loving CS student with a bit of contest math background, but little experience in formal proof writing or anything beyond basic probability.
The course is divided into two parts: Discrete Mathematics and Probability Theory (as can probably be inferred by my previous 2 references to the cla…