Understanding Probabilities: Proving P(A/B)=1 and A, B Independence

In summary, the person is asking for help with two questions related to probabilities and intersections. The first question is about proving a statement involving P(A/B) and P(B compl. / A compl.), while the second question involves examining the relationship between two events A and B with non-zero probabilities, and whether they are independent or foreign. The person also mentions posting frequently in order to have a chance to write in final exams.
  • #1
dionys
10
0
Hi again...This is my last question for today.
I know that i send a lot of threads but...i don't have anyone else to help me.

Most of the times i don't send any solutions.I try but sometimes i don't understand and so...i don't have something to write.I post frequently
because if i don't give a 50% of correct answers i will not have the chance to write in the final exams...its a stupid rule.

My last 2 questions for today are.

1.We must prove that if P(A/B)=1 then P(B compl. / A compl.)=1
i wrote a lot of things but ..i didnt prove nothing : ~)

2.A and B are two events with non zero probabilities.
I must show (prove) if the following are i)correct,ii)faulse iii)correct under some conventions.
a)if A and B are foreign then they are independent (i don't know if this is the correct word) butif they are foreign P(A[intersect]B)=[empty-set]
b)if A and B are independent then they are foreign
c)P(A)=P(B)=0.6 A,B are foreign
c)P(A)=P(B)=0.6 A,B are independent
 
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  • #2
for 1>
what is the basic definition of P(A/B) ??
(There is one in terms of intersections!)
once u have this, simply work through it...

for 2>
what u have done with this so far?

-- AI
 
  • #3


Hi there,

I understand your concern about needing to give correct answers in order to have the chance to write in the final exams. I will do my best to help you understand these concepts so that you can confidently answer questions in your exams.

For your first question, we need to prove that if P(A/B) = 1, then P(B complement/A complement) = 1. To do this, we can use the definition of conditional probability: P(A/B) = P(A and B)/P(B). Since P(A/B) = 1, this means that P(A and B) = P(B). Now, using the definition of conditional probability again, we can say that P(B complement/A complement) = P(B complement and A complement)/P(A complement). Since we know that P(A and B) = P(B), this means that P(B complement and A complement) = P(A complement). Now, using this information, we can say that P(B complement/A complement) = P(A complement)/P(A complement) = 1. Therefore, we have proven that if P(A/B) = 1, then P(B complement/A complement) = 1.

For your second question, we need to consider the relationship between independence and disjoint events. If two events are disjoint, this means that they cannot occur at the same time. In other words, if one event happens, the other event cannot happen. On the other hand, if two events are independent, this means that the occurrence of one event does not affect the probability of the other event occurring.

a) If A and B are disjoint, then it is not possible for them to be independent. This is because if one event occurs, the other one cannot occur, and therefore the occurrence of one event does affect the probability of the other event occurring. So, the statement is false.

b) If A and B are independent, then they cannot be disjoint. This is because if the occurrence of one event does not affect the probability of the other event occurring, then it is possible for both events to occur at the same time. So, the statement is also false.

c) If A and B are both foreign (I believe you meant to say "disjoint" here), then this does not necessarily mean they are independent. Disjoint events cannot occur at the same time, but this does not mean that the occurrence of one event does not affect the probability of the other event occurring. So
 

1. What is probability?

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

2. How do you calculate probabilities?

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical definition of probability.

3. What are the different types of probabilities?

There are three main types of probabilities: theoretical, experimental, and subjective. Theoretical probability is based on mathematical calculations, experimental probability is based on observations and data, and subjective probability is based on personal beliefs or opinions.

4. How can probabilities be used in real life?

Probabilities are used in many practical applications, such as weather forecasting, risk assessment, and decision making. They can also be used in gambling, insurance, and sports predictions.

5. Can probabilities change?

Yes, probabilities can change based on new information or events that affect the likelihood of an outcome. This is known as conditional probability, where the probability of an event is dependent on the occurrence of another event.

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