Introduction to Probability
Probability and odds are two ways of expressing the likelihood of something being true or happening. There are some slight subtle differences between the two, but it’s good to understand both. Most people have an intuitive feel for probability, and if you’re a betting man or woman, I’d put a 2 to 1 bet down that you understand odds as well.
- Probability = (# outcomes we want) / (# all possible outcomes)
- Odds = (# outcomes we want) / (# all possible OTHER outcomes)
We’ll cover odds in the next video.
Introduction to Odds
Odds are the other way for calculating likelihood. While the values for probability range from 0 to 1, odds can range from 0 to infinity. Odds are sometimes written like 4:1 (pronounced 4-to-1), 0.2:1 or 1:1 (even odds).
Even chances (like getting heads with a fair coin) are expressed in probability as 50% (or 0.5) and expressed in odds as 1:1 (or just 1).
You can even convert between probability and odds, if you’re so inclined:
- odds = probability / (1-probability)
- probability = odds / (1+odds)
The Multiplication & Addition Rule
In this video we differentiate between independent and dependent events. With dependent events, the probability of one event depends on what you did before. We also look at the multiplication and addition rule.
- multiplication rule: if you want to know the probability of something happening AND something else happening, you multiply their individual probabilities
- addition rule: if you want to know the probability of something happening OR something else happening, you add their individual probabilities
Let me provide an example of a dependent event, to help clarify. An example of a dependent event is having the second draw from a deck of cards be a diamond. If the first card you draw is a diamond, there are only 12 diamonds left in the deck when you pick the second card. If the first card was not a diamond, there are still 13 diamonds left in the deck. So the probability of pulling a diamond on the second is dependent on the first draw.
The binomial theorem
The binomial theorem is way of expanding binomials (remember algebra? don’t worry, you don’t have to). You can then use these expanded binomials to help you calculate probabilities of independent events. Basically, if someone asked you “If I have 6 kids, what’s the probability that I would have 2 boys and 4 girls?” you could use this trick. If this makes no sense, don’t worry. Watch the video and let me know if it still isn’t clear.
WARNING: you will stoke up your inner geek in this video when we learn about Pascal’s triangle
Test your comprehension
With this probability and odds problem set.
patwari 
The problem set is misleading. Most of the questions are unanswerable because the population of the Little Italy area is undefined. We have nt defined a number of people at risk for developing hallucinations. You can’t just use the total number of people in the ER as if it were representative of the total population of Chicago or of the Little Italy Neighborhood. If 9% of the people in the ER came in with gunshot wounds, that does not mean that you have 1:10 odds of getting shot that day in Chicago.
I rest my case.
Joji, thank you for your comments. the population to consider in the problem set is the people who present to the ER. While there may be some inconsistencies with the logic of the problem, I think it’s safe to say you have to suspend your disbelief in this problem — given that people are developing magical powers. We’re aiming at the mathematical skills, here. Let me know if that helps.