What is P(B) given P(A|~B) = 1/2 and P(B?AUB) = 2/5?

In summary, the conversation is about finding the probability of event B given certain conditions. The given information includes P(A|~B) = 1/2 and P(B?AUB) = 2/5, where ~B means not B. The formula for conditional probability is also mentioned. However, there is some confusion regarding the notation P(B?AUB) = 2/5. The person asking for help is looking for guidance on how to solve for P(B), with the final answer being 1/4.
  • #1
Yankel
395
0
Hello all

I have a little problem with this short question, would appreciate your help.

Let A and B be two events such that:

P(A|~B) = 1/2 and P(B?AUB) = 2/5

(~B means not B)

Find P(B)

The final answer should be 1/4, I can't get there. I did some work with the conditional probability formula, got P(B)=2/5 * P(AUB) and P(B)=1-2*P(A and ~B). But where do I go from here ?

Thank you in advance !
 
Mathematics news on Phys.org
  • #2
Hi Yankel!

I'm not sure what you mean by this: P(B?AUB) = 2/5. Could you explain? It's the question mark that's confusing me.

Anytime I see the phrase "conditional probability" I always write out the formula: \(\displaystyle P[A|B]=\frac{P[A \cap B]}{P}\).

In this case we're given: \(\displaystyle P[A|B']=\frac{P[A \cap B']}{P[B']}=\frac{1}{2}\).

So if you can explain my above question I'll try to help more. :)
 

FAQ: What is P(B) given P(A|~B) = 1/2 and P(B?AUB) = 2/5?

What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is expressed as P(A|B), where A is the event of interest and B is the event that has already occurred.

How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the joint occurrence of both events by the probability of the first event. This can be expressed as P(A|B) = P(A and B) / P(B).

What is the difference between conditional probability and unconditional probability?

Unconditional probability is the likelihood of an event occurring without any prior knowledge or information. On the other hand, conditional probability takes into account the occurrence of another event when calculating the likelihood of the event of interest.

What are some real-life applications of conditional probability?

Conditional probability is commonly used in fields such as insurance, finance, and medicine. It can be used to calculate the likelihood of a disease given a positive test result, or the probability of an accident given certain driving conditions.

How does Bayesian inference relate to conditional probability?

Bayesian inference is a statistical method that uses conditional probability to update beliefs or predictions based on new evidence. It involves updating the probability of a hypothesis based on prior knowledge and new information.

Similar threads

Replies
2
Views
3K
Replies
6
Views
3K
Replies
4
Views
1K
Replies
3
Views
2K
Replies
1
Views
1K
Back
Top