Probability: Independent vs. Dependent events

[trojansc82]

Homework Statement

2. Let a random experiment be the cast one “six-sided” die and one “four-sided” die.

(a) Give an example of two independent events and justify your answer.
(b) Give an example of two dependent events from this sample space and justify your answer.

Homework Equations

Independent event:
P(A ∩ B) = P(A) * P(B|A) = P(A) * P(B)

Dependent event:

Not Independent, i.e. P(A) * P(B) = P(A ∩ B)

The Attempt at a Solution

A = {(1,1), (1,2)}

B = {(1,1), (2,1)}

P(B) = P(B|A) = P(A ∩ B)/P(A) = (1/24)/(2/24) = 1/2

P(B) is not equal to 1/2

 

[Mark44]

Homework Statement

2. Let a random experiment be the cast one “six-sided” die and one “four-sided” die.

(a) Give an example of two independent events and justify your answer.
(b) Give an example of two dependent events from this sample space and justify your answer.

Homework Equations

Independent event:
P(A ∩ B) = P(A) * P(B|A) = P(A) * P(B)

Dependent event:

Not Independent, i.e. P(A) * P(B) = P(A ∩ B)

The Attempt at a Solution

A = {(1,1), (1,2)}

B = {(1,1), (2,1)}

P(B) = P(B|A) = P(A ∩ B)/P(A) = (1/24)/(2/24) = 1/2

P(B) is not equal to 1/2

No one has replied, possibly because your work is so terse, making it difficult to understand.

Are A and B the two events? What do they represent (in words)?

On one line you say that P(B) = 1/2, and on the next line you say that P(B) is not equal to 1/2. How can a given probability be equal to and also not equal to the same number?