Khan Academy on a Stick
Probability and combinatorics
Permutations and combinations. Using combinatorics to solve questions in probability.
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Permutations
Introduction to permutations
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Combinations
Introduction to combinations
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Example: Ways to arrange colors
Thinking about how many ways you can pick four colors from a group of 6
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Example: 9 card hands
Thinking about how many ways we can construct a hand of 9 cards
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Example: Ways to pick officers
How many ways can we pick officers for our organization?
Permutations and combinations
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? What if you don't care what order they are in or how they are posed (okay, of course you care about their awesome poses)?
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Example: Probability through counting outcomes
The probability of getting exactly 2 heads when flipping three coins. Thinking about this by visualy depicting all of the outcomes.
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Example: All the ways you can flip a coin
Manually going through the combinatorics to determine the probability of an event occuring
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Getting exactly two heads (combinatorics)
A different way to think about the probability of getting 2 heads in 4 flips
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Probability and combinations (part 2)
Making at least 3 out of 5 free throws.
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Probability using combinations
Probability of getting exactly 3 heads in 8 flips of a fair coin.
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Exactly three heads in five flips
Probability of exactly 3 heads in 5 flips using combinations
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Example: Different ways to pick officers
Thinking about the different ways we can pick officers in order to find the probability of one situation in particular.
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Example: Combinatorics and probability
Probability of getting a set of cards
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Example: Lottery probability
What is the probability of winning a 4-number lottery?
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Mega millions jackpot probability
Probability of winning the Mega Millions jackpot
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Generalizing with binomial coefficients (bit advanced)
Conceptual understanding of where the formula for binomial coefficients come from
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Conditional probability and combinations
Probability that I picked a fair coin given that I flipped 4 out of 6 heads.
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Conditional probability warmup
Conditional probability visualized using trees.
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Birthday probability problem
The probability that at least 2 people in a room of 30 share the same birthday.
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.
Simple hypothesis testing
Picking fairly