A few basic probability concepts

In summary, the conversation discusses the frustration with writing out all possible outcomes in a random experiment and the desire for alternative methods of calculating probabilities without unnecessary work. The use of combinations is suggested as a more efficient approach.
  • #1
KingNothing
882
4
Hi...we are doing this now in math. Our teacher insists on writing every possible outcome in a random experiment, which is proposterous. Why write out and literally count something that is fully calculable?

I can get some things pretty well. We'll have questions like "4 coins are flipped" with "what are the chances that there will be at least 2 heads"?

Well...we also have some with dice...like rolling two d6's, what are the chances that the sum of the two numbers will be 4-7 inclusive? I know what the answer is, but how would you get it with just math? I think it would invlolve factorials.

Please..tell me EVERYthing there is to know about calculating probabilities with a set of so many given outcomes, etc.
 
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  • #2
Originally posted by Decker
Hi...we are doing this now in math. Our teacher insists on writing every possible outcome in a random experiment, which is proposterous. Why write out and literally count something that is fully calculable?

I can get some things pretty well. We'll have questions like "4 coins are flipped" with "what are the chances that there will be at least 2 heads"?

Well...we also have some with dice...like rolling two d6's, what are the chances that the sum of the two numbers will be 4-7 inclusive? I know what the answer is, but how would you get it with just math? I think it would invlolve factorials.

Please..tell me EVERYthing there is to know about calculating probabilities with a set of so many given outcomes, etc.

Didn't you just tell us that you DON'T WANT to know "EVERYthing". Otherwise you would be quite happy to "write every possible outcome" and wouldn't consider it preposterous.

Yes, I understand what you are saying: It is preposterous that your teacher would expect you to do a lot of work in order to understand what's happening when it is so much easier to just memorize formulas (what you clearly mean by "just math") rather than actually having to learn mathematics.
 
  • #3
No, you misunderstand. And your implication of my simplicity is just rude. I understand why algorithms and formulas work just fine. I know why 1-((5/6)^2) yields the same result as making a huge table displaying every combination and counting all the outcomes of rolling two dice that are one number or another.

That's why I want to know other ways to do them without any unnecessary work. Unnecessary work is bad when it doesn't help you at all. Please don't imply that I don't understand them.

To put it simply, I am at a point where I understand why formulas/calculations work, and I understand quite well 95% of the time. That's why I want to know ways of doing it like that. To save resources.

I don't know why you had to go off and make implications.
 
  • #4
You are quite right in thinking it has to do with factorials :smile:
So, instead of writing out all those nasty sample points, let's just use combinations. In your exapmle of tossing 4 coins : Let A denote the event of abtaining exactly 2 heads

[tex] C^4_2 = 4! / [(4-2)! * 2!] [/tex]

You will find that most of the time combinations will be your best bet. Hope I'm not going to get flamed for posting this.
 

1. What is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. What is the difference between independent and dependent events?

Independent events are events that have no impact on each other, meaning the outcome of one event does not affect the outcome of the other. Dependent events, on the other hand, are events where the outcome of one event does affect the outcome of the other.

3. How is probability calculated?

Probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes. This can be represented as a fraction, decimal, or percentage.

4. What is the difference between theoretical and experimental probability?

Theoretical probability is the probability of an event occurring based on mathematical calculations and assumptions. Experimental probability, on the other hand, is the probability of an event occurring based on actual observations and data.

5. How can probability be used in everyday life?

Probability can be used in everyday life to make informed decisions and predictions. It can be used in fields such as finance, weather forecasting, and sports predictions. Understanding probability can also help in evaluating risk and making sound decisions.

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