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### 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
• Say your cat ate ur computer, then ur science project ate ur cat
• Does probability help in real-life situations? If yes, how?
• Probability is the chance that basically anything can happen.

It is helpful in real-life situations because you can come up with the likeliness that it will or will not happen.

Probability is used for so many things. The weather is a good example. When you see the weather, it's all in probabilities. 20% chance for rain or a 50% chance of snow or a 10% chance of hail.
It's also very important in the stock markets, in gambling, in decision making, and many of the sciences!

An example:

// A doctor in an emergency room has to think very quickly when a patient comes in with a rare condition.

When he looks at the statistics, he determines there is a (1/10) chance the patient will survive unless he performs surgery. OR, a (9/10) chance the patient will die without surgery.

The surgery has a (9/10) chance of success, OR a (1/10) chance of failure.

The patient has the same chance of miraculously surviving without any medical intervention (which is 1/10) as they do with the surgery failing (which is 1/10), OR, they have a (9/10) chance of surviving if they allow the doctor to perform surgery.

Although this is very watered down and simplified, it's a good conceptual beginning. The actual variables and factors that can go into real-life scenarios is very complex and it can become very difficult very quick.
• 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.
• 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.
• At it says if something is 0 then it is impossible, then does that mean if it is 0.00000001 it is impossible but still a tiny bit possible??
• If an event has probability 0.00000001, it is possible but extremely unlikely to happen.

Have a blessed, wonderful day!