# Probability and combinatorics

Contents

Basics of probability and combinatorics

Flip a quarter a hundred times. What's the probability that it will turn up heads? Tails? Even if we are unsure about whether something will happen, we can start to be mathematical about the "chances" of an event (essentially realizing that some things are more likely than others) occurring. This tutorial will introduce us to the tools that allow us to think about random events and the logic behind comparing, judging, and finding the probabilities of those events.

What is the probability of getting a diamond or an ace from a deck of cards? Well I could get a diamond that is not an ace, an ace that is not a diamond, or the ace of diamonds. This tutorial helps us think these types of situations through a bit better (especially with the help of our good friend, the Venn diagram).

What is the probability of making three free throws in a row (LeBron literally asks this in this tutorial).
In this tutorial, we'll explore compound events happening where the probability of one event is not dependent on the outcome of another (compound, independent, events).

See how we can use the multiplication rule to find the compound probability of independent events.

What's the probability of picking two "e" from the bag in scrabble (assuming that I don't replace the tiles). Well, the probability of picking an 'e' on your second try depends on what happened in the first (if you picked an 'e' the first time around, then there is one less 'e' in the bag). This is just one of many, many type of scenarios involving dependent probability.

You want to display your Chuck Norris dolls on your desk at school and there is only room for five of them. Unfortunately, you own 50. How many ways can you pick the dolls and arrange them on your desk?

You are already familiar with calculating permutation ("How many ways could 7 different people sit in 4 different seats?"). But what if you didn't care about which seat they sat in? What if you just cared about which 4 people were in the car? Or put another way, you want to know how many combinations of 4 people can you stick in the car from a pool of 7 candidates. Or how many ways are there to choose 4 things from a pool of 7? Look no further than this tutorial to answer your questions.

This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better "investments" than poring all your money into the Powerball Lottery.