Question

What must be true for P (A and B) = P (A) * P (B)?

Answer 1

now that is "independent"

Answer 2

because it says AND

Answer 3

because by definition , \(A\) and \(B\) are "independent" if
\[P(A)=P(B|A)=\frac{P(A\cap B)}{P(B)}\]

Answer 4

this is the same as saying
\[P(A)P(B)=P(A\cap B)\]

Answer 5

oh my goodness that is confusing, but I understand

Answer 6

"independent" and "disjoint" are two completely different concepts

Answer 7

here is an example
if you flip a coin once and then flip it again, those events are "independent" because the second flip is not influenced at all by the first

Answer 8

whereas if you roll a die once, you cannot get both a "1" and a "2" so those events are "disjoint"

Answer 9

but it says and so an example would be you have 2 red marbles and 2 white, if you take out a red and not put it back whats the probability of taking out a white next?

Answer 10

is that right? or am I completely wrong