Basic probability confusion with independence

[Jeff_McD18]

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?

 

[tiny-tim]

Welcome to PF!

Hi Jeff! Welcome to PF!

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.

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.

 

[Jeff_McD18]

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

How would you go about solving p(B|A)?

 

[tiny-tim]

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

No.

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

 

[Jeff_McD18]

P(A|B) = p(A n B)/p(B)

 

[tiny-tim]

Aha!

ok … so applying it, P(A|B) = … ?