Probability Proof: P(Ai)>0 for i=1-n, P(B)>0

Easy16 · 2009-04-08T09:21:57+00:00

P(Ai)>0, for i=1,2,...n. P(B)>0. Show that if P(A1lB) P(Ai), for at least 1 value of i.

Thread starter Easy16
Start date Apr 8, 2009
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Probability Proof

In summary, P(Ai)>0 for i=1-n means that the probability of event Ai occurring is greater than 0, for all values of i from 1 to n. P(B)>0 means that the probability of event B occurring is also greater than 0. This condition is important because it ensures that the events Ai and B have a non-zero chance of occurring. P(Ai)>0 for i=1-n and P(B)>0 are both conditions that must be met in order for the probability proof to be valid. They show that there is a non-zero probability for both individual events (Ai and B) to occur. To calculate the probability of a specific outcome, you would need to use additional information such as

Apr 8, 2009

Easy16

P(Ai)>0, for i=1,2,...n. P(B)>0. Show that if P(A1lB)<P(A1), then P(AilB)>P(Ai), for at least 1 value of i.

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Apr 8, 2009

mathman

Science Advisor

If you assume Ai are disjoint and the all Ai's fill up the sample space, then it is easy.
Sum of P(Ai)=1 and Sum P(Ai|B)=1. You should be able to do the rest.

Related to Probability Proof: P(Ai)>0 for i=1-n, P(B)>0

1. What is the meaning of "P(Ai)>0 for i=1-n, P(B)>0" in probability proof?

P(Ai)>0 for i=1-n means that the probability of event Ai occurring is greater than 0, for all values of i from 1 to n. P(B)>0 means that the probability of event B occurring is also greater than 0.

2. Why is it important for P(Ai)>0 for i=1-n, P(B)>0 in probability proof?

This condition is important because it ensures that the events Ai and B have a non-zero chance of occurring. Without this, the probability proof would not be valid and would not accurately represent the likelihood of these events happening.

3. What is the relationship between P(Ai)>0 for i=1-n and P(B)>0 in probability proof?

P(Ai)>0 for i=1-n and P(B)>0 are both conditions that must be met in order for the probability proof to be valid. They show that there is a non-zero probability for both individual events (Ai and B) to occur.

4. How do you use P(Ai)>0 for i=1-n, P(B)>0 in probability proof to calculate the probability of a specific outcome?

To calculate the probability of a specific outcome, you would need to use additional information such as the sample space and the number of possible outcomes. P(Ai)>0 for i=1-n and P(B)>0 simply ensure that the probability of any outcome is not equal to 0, but they do not provide the exact probability of a specific outcome.

5. Can P(Ai)>0 for i=1-n, P(B)>0 be applied to any type of probability proof?

Yes, this condition can be applied to any type of probability proof as it is a fundamental requirement for any probability calculation. Without this condition, the probability proof would not be valid.