SOLUTION: Hello! Suppose A is a subset of B and that P(A)>0 and P(B)>0. Are A and B independent? Prove your answer? Thank you

Algebra.Com
Question 349530: Hello!

Suppose A is a subset of B and that P(A)>0 and P(B)>0. Are A and B independent? Prove your answer?

Thank you

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Hint: Ask yourself this question: Is P(A | B) = P(A) and is P(B | A) = P(B) ?

Note: P(A | B) means "Probability of event A happening given that event B has already happened"


In other words, if event A happens, does that affect/change the probability of event B from happening (or vice versa)?


RELATED QUESTIONS

Prove that if V and W are two independent events such that V is a subset of W, then... (answered by oscargut)
A and B are independent events. P(B) = 0.5 and P(A AND B) = 0.3. Find P(A). Round your (answered by ikleyn)
Suppose P(A) = 0.25 and P(B) =0.15.If A and B are independent events but not mutually... (answered by ikleyn)
Given P(A) = 0.82, P(B) = 0.87, and the fact that events A and B are independent, What is (answered by ikleyn)
Assume that P(A) = 0.7, P(B) = 0.8, and P(B and A) = 0.56. a) Find P(A|B) and P(B|A).... (answered by ikleyn,math_tutor2020)
Given that P(A) = 0.47, P(B) = 0.07, and P(A and B) = 0.0329, are events A and B... (answered by ikleyn)
Suppose P(A)=0.9, P(B)=0.4 and P(B|A)=0.2. What is... (answered by math_tutor2020)
If P(A) > 0, P(B) > 0 and P(A) < P(A|B), show that P(B) < P(B|A) Thank... (answered by ikleyn)
Let A be a finite set, and define by f: P(B) -> N(non-negative integers) by f(B) = |B|. (answered by ikleyn)