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Lesson 1: Basic probability

# Intuitive sense of probabilities

Think about what probabilities really mean. What does a probability of 0 mean? How about 1?

## Want to join the conversation?

• At , how is .99999 repeating equal to one? It rounds to one, but how does that make it the same thing? •   Let's think about it. First, we have to understand that the 9's go on forever, so they don't just stop after a while. Now, can you think of any number that would fit between 0.9 repeating and one? 0.1? 0.001? Any of the numbers if added to 0.9 repeating would go over one. Therefore, there are no numbers that can be slipped between 0.9 repeating and one, and therefore the two numbers are the same.

We can also prove this algebraically.
Let `x = 0.999...` (repeating)
`10x = 9.999...`
`10x - x = 9.999... - 0.999...`
`9x = 9`
`9x/9 = 9/9` Any number over itself (except zero) is one.
`x = 1`

We just proved that 0.999... is equal to one. Another helpful thing to remember is that a number can have (at least) two decimal representations: 1 = 0.999...; 5 = 4.999... etc.
• I very much dislike this • who here is being forced to do this dumb stuff in school
(also, anyone remember prodigy?)  • The probability that my cat Nadia can write a phenomenal novel is 1! :) She's an awesome cat and can do anything! • Based on my understanding, a probability of 0 means "it's technically possible, but don't hold your breath expecting it to happen." Like a dart hitting the exact center of a dartboard (an infinitesimally small point) or a dart hitting the exact edge of a dartboard (another infinitesimally small point).
But I'm not sure how to translate that understanding into the dice example. Could someone help clarify? • Well,if an event is technically possible, it means the event has a probability close to zero, not exactly zero. It will be very close to zero, surely, but not exactly zero, which is a very important difference. The probability of a dice showing six 1000 times in a row or a dart hitting the exact center of a dartboard are events with almost zero probability but the probability of a dice showing 7 or a dart becoming invisible are events with exactly zero probability. If an event has zero probabilty, it is impossible, technically or otherwise. Any event which is possible, no matter how unlikely it is, will have non-zero probability.
• oh real real • I know this doesn't really have much of anything to do with probability but what are the chances of getting struck by lightning and having all those extra electrons trapped in your body coursing through your veins all in circles and rubbing together creating a lot of friction in your body that usually creates lightning in the sky but instead giving u lightning abilities that you have to adapt to controlling it with your cells in your body? Could someone please explain how that doesn't make sense or is impossible? I'm really curious how. Even though I know it sounds a bit stupid.   