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## Statistics and probability

### Course: Statistics and probability>Unit 7

Lesson 1: Basic theoretical 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?)   • oh real real • 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.
• In this video as you can see above this comment, I'll summarize the video in a shorter way.
1: You are rolling a die. (6 sides) how much possibilites are there? (6 as well)
2: What is the probability of rolling a number greater than 2 and smaller than 5? Well, there are only 2 numbers on a number die that are larger than 2 and smaller than 5. They are 3, and 4. That is 2 out of 6 so the answer would be 2/6.
3: Say you have an fair coin. What chance, (In percentage) would be heads? (The answer, 50%)
if the probability (chance) is impossible, than the chance of whatever impossible event you thought up is 0%. If someone said, "What's the chance that the sun will rise tommorow?" You would say, "100% chance, because it's guarrented. You know the sun will rise no matter what. Unless an unpredicted event like the metiorite crashes into earth changes things. The earth could be knocked out of the gravitional pull of the sun, and then you would not see the sun rise, because you might be in another solar system, orbiting a different star you call, like, Balvita or something. Then the sun would not rise. If you say, "No, they're still orbiting a sun," Then remember, the sun is a star, and the sun is just a name for a particular star. So all the other stars are not called the Sun. So, the chance of the sun rising would be zero. While it is most likley impossible for a comet flying straight a earth going unnoticed, we always have to take into effect interspacial activity. If you ever are calculating space probability when you grow up, remember to take into consideration the unpredictable-ness of space. This was not copied from the transcript. I, EK/Kodi🐺🦊, typed this myself. I hope this helps you. If you need more help, please respond and I will do what I can. I typed that I typed this myself because some people will not beleive me, as I have copied the Transcript for fun below. So there is currently suspicion directed at me. Do not be alarmed. It's not serious. It was for fun. On that note, ask for help if you need it. There are many people in Khan Academy, Including me, willing to help you if you need it. So just ask!   