Trigonometry and precalculus
Venn diagrams and the addition rule
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).
Compound, independent events
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).
- Compound Probability of Independent Events
- Getting At Least One Heads
- Example: Probability of rolling doubles
- LeBron Asks: What are the chances of making 10 free throws in a row?
- LeBron Asks: What are the chances of three free throws versus one three pointer?
- Frequency Probability and Unfair Coins
- Example: Getting two questions right on an exam
- Example: Rolling even three times
- Independent probability
Dependent 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.
Permutations and combinations
If 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? What if you don't what order they are in or how they are posed (okay, of course you care about their awesome poses)?
Probability using combinatorics
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.
- Example: Probability through counting outcomes
- Example: All the ways you can flip a coin
- Getting Exactly Two Heads (Combinatorics)
- Probability and Combinations (part 2)
- Probability using Combinations
- Exactly Three Heads in Five Flips
- Example: Different ways to pick officers
- Example: Combinatorics and probability
- Example: Lottery probability
- Mega Millions Jackpot Probability
- Generalizing with Binomial Coefficients (bit advanced)
- Conditional Probability and Combinations
- Birthday Probability Problem
- Probability with permutations and combinations