Basic probability confusion with independence

In summary, based on the given statements, we can determine that the probability of A given B is 1/3 and the probability of B given A is also 1/3. This is determined by the fact that B is a subset of A and therefore the probability of B is equal to the probability of A given B.
  • #1
Jeff_McD18
11
0
Q. Consider the following statements about events A, B, and C.

- p(A) = 2/3
- p(B) = 1/2
- B c A
- Events A and C are independent
- Events B and C are mutually exclusive

Given that B is a subset of A is what is P(A n B). B is completely contained in A so any point in B is also in A which means that (A n B) = B which implies P(A n B) = P(B).

so therefor p(A|B) = 1/3

&

p(B|A)= 1/3

Is this correct?
 
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  • #2
Welcome to PF!

Hi Jeff! Welcome to PF! :wink:
Jeff_McD18 said:
Given that B is a subset of A is what is P(A n B). B is completely contained in A so any point in B is also in A which means that (A n B) = B which implies P(A n B) = P(B).

Yes. :smile:
so therefor p(A|B) = 1/3

&

p(B|A)= 1/3

No.

p(A|B) is pronounced "the probability of A given B", and means the probability that something in B is also in A.
 
  • #3


okay, so p(A|B)=p(B)=1/3

How would you go about solving p(B|A)?
 
  • #4
Jeff_McD18 said:
okay, so p(A|B)=p(B)=1/3

No.

Don't you know a formula for P(A|B) ?
 
  • #5


P(A|B) = p(A n B)/p(B)
 
  • #6
Aha! :smile:

ok … so applying it, P(A|B) = … ? :wink:
 

FAQ: Basic probability confusion with independence

What does independence mean in relation to probability?

Independence means that the occurrence of one event does not affect the probability of another event happening. In other words, the two events are not related or influenced by each other.

How can I tell if two events are independent?

If two events are independent, the probability of one event occurring does not change based on whether the other event has occurred or not. In mathematical terms, if P(A) and P(B) are the probabilities of two events A and B, then P(A|B) = P(A) and P(B|A) = P(B).

Can two events be independent and dependent at the same time?

No, two events cannot be both independent and dependent at the same time. They are mutually exclusive concepts. If two events are independent, they cannot be dependent on each other.

What is the difference between independent and mutually exclusive events?

Independent events have no influence on each other's probabilities, while mutually exclusive events cannot occur at the same time. For example, rolling a "3" on a dice and getting a head on a coin toss are independent events, but rolling an "odd number" and rolling a "2" are mutually exclusive events.

How can I use the concept of independence in real-life situations?

Understanding independence in probability can be useful in many real-life situations, such as predicting the outcomes of experiments or events. It can also help in making informed decisions, for example, in business or finance, by considering the independence of different variables and their impact on each other.

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