Solving a Probability Problem: Get Help Here

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In summary, the speaker is trying to calculate the probability of getting at least 1, 2, 3, etc. desired results in 7 separate macro-events. They are using a tree diagram to represent the different possible outcomes and calculating the probability by multiplying the probabilities at each branch point. They also mention the concept of independence and how it relates to probability calculations.
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Nex Vortex
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I'm trying to figure out the probability of getting something tomorrow, but since I've never taken a statistics course, I don't really know how to do a problem of this nature.

There are two events, I will call the macro-events, M and N for argument sake, each with a 50% chance of happening. In each macro-event, there are also three micro-events, I will call M1, M2, M3, N1, etc. Each micro-event has a 20% chance of a desired result. After a desired result is reached, it cannot be gotten again. I will run 7 separate macro-events. I was curious of the probability that I will get at least 1, 2, 3, etc. desired results.

For example, if the first macro-event is M, and I get a desired result for M2, it will not be a desired result for subsequent runs, leaving only M1, M3, N1, etc. for the remaining 6 macro-events.

Can somebody help me out on how to solve a problem of this nature?
Thanks
 
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  • #2
Nex Vortex said:
I'm trying to figure out the probability of getting something tomorrow, but since I've never taken a statistics course, I don't really know how to do a problem of this nature.

There are two events, I will call the macro-events, M and N for argument sake, each with a 50% chance of happening. In each macro-event, there are also three micro-events, I will call M1, M2, M3, N1, etc. Each micro-event has a 20% chance of a desired result. After a desired result is reached, it cannot be gotten again. I will run 7 separate macro-events. I was curious of the probability that I will get at least 1, 2, 3, etc. desired results.

For example, if the first macro-event is M, and I get a desired result for M2, it will not be a desired result for subsequent runs, leaving only M1, M3, N1, etc. for the remaining 6 macro-events.

Can somebody help me out on how to solve a problem of this nature?
Thanks

Hey Nex Vortex and welcome to the forums.

The most intuitive way to get into probability is to use tree diagrams. A tree diagram has branches that go from left to right and events on the right are based on related events that they "inherit" from on the left.

So I'll start with an example of a coin toss that is done twice.

Your first branch will be two main branches: one a head and one a tail. For the head and the tail it will have two branches both a head and a tail. Counting up all the leaves (things with no more branches) you have four events.

The way to calculate a probability for some event (leaf) is to multiply the probabilities at each branch point. Let's say we have a fair coin with equal chance of getting a head or a tail. The probability of getting two heads is 1/2 x 1/2 = 1/4.

Now we could say that because of independence that its easier to use binomial distribution with 2 trials and p = 1/2, but that's not the point of the tree diagram. The point of the tree diagram is to show you how to think about any probability independent or not.

If you are doing events based on time of occurrence (like the coin toss) go from left to right. You should note that at any level of the branch, all leaves in that level have to equal one: the reason is that if they don't then if it is less than one, you have missed out some possible event and if it is greater than one then you have made a mistake.

So start off with your first possible events as your first branches, make sure they add up to 1. Then do your sub-events and make sure all leaves at that level add to one, and repeat until you've gone to whatever level.

Once you've got your tree diagram multiply probabilities at each node right up till the leaf and that is your probability for that event. Note that if you get some events that are dependent on other events happening, this will be reflected in your tree diagram.

So to recap:

1) Draw a tree diagram with each node of the tree being some atomic event (can't divide it any further)
2) Assign a probability to each node
3) Make sure total of all probabilities at a specific tree depth add up to 1
4) For a given event at a particular leaf node multiply all node values from leaf all the way up to trunk to get final probability

and you're done
 

1. What is a probability problem?

A probability problem is a mathematical question that involves determining the likelihood or chance of a certain event or outcome occurring. It usually involves calculating the ratio of favorable outcomes to all possible outcomes.

2. How do I approach solving a probability problem?

The first step in solving a probability problem is to clearly define the event and all possible outcomes. Then, use the appropriate formula or method to calculate the probability. It is important to also check for any assumptions or conditions that may affect the outcome.

3. What are some common techniques for solving probability problems?

Some common techniques for solving probability problems include using probability trees, the fundamental counting principle, and the addition and multiplication rules of probability. Other methods, such as Bayes' theorem and combinatorics, may also be useful in certain situations.

4. What are some common mistakes to avoid when solving a probability problem?

Some common mistakes to avoid when solving a probability problem include forgetting to consider all possible outcomes, using incorrect formulas or calculations, and making assumptions without proper justification. It is also important to check for any biases or errors in the data used.

5. Where can I get help with solving a probability problem?

You can get help with solving a probability problem from various sources such as textbooks, online tutorials and practice problems, and consulting with a tutor or teacher. Additionally, there are many online forums and communities where you can ask for assistance or clarification on specific probability problems.

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