What Are the Tests for Independence in Probability Statistics?

[Biochemgirl2002]

Homework Statement

2. Let A and B be events with P(A) = 0.5, P(B) = 0.3 and P(A
and B) = 0.8.
A. Find P(A∩B).
B. Are A and B independent events? Explain.
C. Are A and B mutually exclusive? Explain.

Relevant Equations

P(A or B) = P(A)-P(B)

A) (0.5)-(0.3)
=0.2

b)
c) i have no clue how to determine from just a set of numbers if they are independant or mutually exclusive

 

[tnich]

Homework Statement: 2. Let A and B be events with P(A) = 0.5, P(B) = 0.3 and P(A
and B) = 0.8.
A. Find P(A∩B).
B. Are A and B independent events? Explain.
C. Are A and B mutually exclusive? Explain.
Homework Equations: P(A or B) = P(A)-P(B)

A) (0.5)-(0.3)
=0.2

b)
c) i have no clue how to determine from just a set of numbers if they are independant or mutually exclusive

The first thing you need to do is look up some definitions.
What does ##P(A\cap B)## mean? (Hint: It does not mean ##P(A \text{ or } B)##.)
What does it mean for events to be independent?
What does it mean for events to be mutually exclusive?

 

[Biochemgirl2002]

The first thing you need to do is look up some definitions.
What does ##P(A\cap B)## mean? (Hint: It does not mean ##P(A \text{ or } B)##.)
What does it mean for events to be independent?
What does it mean for events to be mutually exclusive?

i think i believe that it means only the intercept between a and b
which i found out was actually zero

if there is no intercept then they are mutually exclusive,

now that i know this . i am still having trouble understanding if they are independant
i found this website (https://www.zweigmedia.com/RealWorl...t for Independence,if not, they are dependent.) where they say that if they don't follow those 3 equations they are dependant, and so i believe it is dependant

 

[tnich]

i think i believe that it means only the intercept between a and b
which i found out was actually zero

if there is no intercept then they are mutually exclusive,

now that i know this . i am still having trouble understanding if they are independant
i found this website (https://www.zweigmedia.com/RealWorld/tutorialsf15e/frames7_5C.html#targetText=Test for Independence,if not, they are dependent.) where they say that if they don't follow those 3 equations they are dependant, and so i believe it is dependant

Right, ##P(A\cap B)## is the probability of the intersection of events (sets) ##A## and ##B##, and you are correct that if that probability is zero then the events are mutually exclusive.
The tests for independence that you found are correct, and the events are independent. The key concept here is that events are independent if knowing whether one occurred does not change the probability that the other occurred. That is the meaning of ##P(A|B)= P(A)##; the probability of ##A## given that you know ##B## has occurred is the the same as the probability of ##A## without knowledge of ##B##.