How to Calculate Probabilities in a Conditional Matrix?

[Paixao]

Hello all,

I am deparing me with a problem or a doubt about the calculation of probabilities in one matrix.

I have 3 events (A,B,C)

Percentage of probability of each event: A - 2.3% B - 10% C - 15%

Conditions:
- A imposes B
- A imposes C

My Matrix:
A B C
0 0 0
0 0 1
0 1 0
0 1 1
1 1 1

Goal: The sum of all lines of matrix must be 100%, the sum of lines of each event must be equal to the percentage of probability given before the matrix generation.

Right now I am changing the percentage of each impose event (A) and I left the imposed event (B,C) with the original percentage.
Thus, I have this changed percentages:

P(A) = P(A|(BxC)) = P(A) / P(B)*P(C) = 1.53 (153%) or could consider 100%
P(B) = P(B) = 0.1 (10%)
P(C) = P(C) = 0.15 (15%)

If I made the calculations with this values, I will obtain 100% for all lines and for all events, but i will obtain negative values because the probability of (A) its bigger than 100%, so (~A)<0.
If i consider 100% instead of 153% I will obtain wrong values for (A) event.

The point is, I am not sure if it is possible to calculate this situation obtaining positive and correct values and I would like to know if anybody have some kind of help or some tips that can help me.

Thank you, and Best Regards.

 

[mmwave]

Hello,

Thank you for sharing your problem with us. I can understand your confusion and would like to offer some suggestions that might help you in your calculations.

Firstly, it is important to note that probabilities cannot exceed 100%. Therefore, your calculation of P(A|(BxC)) as 153% is incorrect. It should be 100% or less. This means that the sum of probabilities for events A, B, and C should not exceed 100%.

In order to achieve this, you can try adjusting the probabilities of events B and C while keeping the probability of A fixed at 2.3%. For example, you can try setting P(B) = 5% and P(C) = 7.5%. This way, the sum of probabilities for events B and C will be 12.5%, which is less than the probability of A (2.3%).

You can also try different combinations of probabilities for events B and C, as long as their sum is less than the probability of A. This will ensure that the sum of probabilities for all events remains 100%.

Additionally, you can use conditional probabilities to calculate the probabilities of events B and C given that event A has occurred. This can be done using the formula P(B|A) = P(A and B) / P(A). Similarly, you can calculate P(C|A) using the same formula. This will help you in adjusting the probabilities of events B and C while taking into account the relationship between event A and events B and C.

I hope these suggestions will be helpful to you. If you have any further questions or need clarification, please feel free to reach out to me. Best of luck with your calculations!

 

[tacman]

Hello,

It seems like you are trying to calculate the probabilities of events A, B, and C while taking into account the conditions that A imposes B and A imposes C. In order to do this, you will need to use conditional probabilities.

Conditional probabilities are calculated by dividing the probability of one event by the probability of another event occurring. In this case, you are trying to calculate P(A | (BxC)) which means the probability of event A occurring given that both events B and C occur. This can be calculated as P(A) / (P(B) * P(C)).

However, as you have noticed, this can result in values greater than 100%. In order to avoid this, you can use the concept of joint probabilities. Joint probabilities represent the probability of two events occurring simultaneously. In this case, you can calculate P(A and B) and P(A and C) separately, and then use these values to calculate P(A | (BxC)) as P(A and B) / P(B) and P(A and C) / P(C).

I would also recommend checking your calculations to ensure that they are correct and that the values add up to 100%. If you are still having trouble, I suggest consulting a statistics textbook or seeking help from a tutor or teacher.

I hope this helps. Best of luck with your calculations!