Sunaina thinks absurd

  Hey, welcome back! This blog post is a continuation of my previous blog post which you can read over  here  . These are just notes and problems.  The handouts/ books I referred to are Evan Chen's  Probability handout  , AOPS introduction to Counting and probability, Calt's  Expected value handout , brilliant and this  IIT Delhi handout. I am reading expected value because it's a prerequisite to the Otis combo unit Global. Hence the name Global Probability." Probability is Global Expected Value:    The expected value is the sum of the probability of each individual event multiplied by the number of times the event happens. It is denoted as $\Bbb E$ $[x]$ We have $$\Bbb E[x]=\sum x_n P(x_n)$$ where $x_n$ is the value of the outcome and $P(x_n)$ is the probability that $x_n$ occurs. Problem 1: What is the expected value of the number that shows up when you roll a fair $6$ sided dice? Solution: Since it's a fair dice, we get each outcom...

 Hey everyone! Welcome back to my blog!  The number of diagonals are $\binom {12}{2}-30=36$ Today we have another topic which I am very scared of, PROBABILITY! I think to overcome this fear, I should start from basics. So, I refer AOPS's introduction to counting and probability. I did till chapter seven and thought to do the rest problems in this blog as notes. The book's pirated copy is available in zlib btw ( I don't think so I should have said this, but I think it's fine). I did the harder problems and wrote the solutions in Xournal. If you want to see them, here is the  pdf . Also both the pdf and following post has amc/ioqm type problems! So enjoy!! Problem 1: $n$ coins are flipped simultaneously flipped. The probability that at most one of them shows tails is $\frac{3}{16}.$ Find $n.$ Solution: We have $$\frac{n+1}{2^n}=\frac{3}{16}\implies 16(n+1)=3\cdot 2^n \implies n\ge 4. $$  But the RHS grows very fast, so $n=5$ is the only solution. Intersection o...