Thread: Independent events

An experiment consists of drawing a number at random from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Let A = {1, 2, 3, 4, 5, 6}, B = {1, 3, 5, 7, 9, 11} and C = {4, 6, 8, 9}.

a) Are A and B independent?
b) Are A and C independent?
c) Are B and C independent?

What does it mean by independent?

The answers say part a) and b) are yes where as c) is no.

Originally Posted by user_5

An experiment consists of drawing a number at random from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Let A = {1, 2, 3, 4, 5, 6}, B = {1, 3, 5, 7, 9, 11} and C = {4, 6, 8, 9}.

a) Are A and B independent?
b) Are A and C independent?
c) Are B and C independent?

What does it mean by independent?

The answers say part a) and b) are yes where as c) is no.

If $\displaystyle P(A\cap B)=P(A)\cdot P(B)$ then $\displaystyle A~\&~B$ are independent.

If $\displaystyle P(B\cap C)\ne P(B)\cdot P(C)$ then $\displaystyle C~\&~B$ are not independent.