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## Homework Statement

Suppose P(A) = .6, P([tex]\overline{A}[/tex] | B) = .4. Check whether events A and B are independent.

## Homework Equations

Two events A and B are said to be independent if P(A|B) = P(A). This is equivalent to stating that P(A [tex]\cap[/tex] B) = P(A)P(B)

If A and B are any two events, then the conditional probability of A given B, denoted by P(A | B), is P(A | B) = [tex]\frac{P(A \cap B)}{P(B)}[/tex] provided P(B) > 0.

## The Attempt at a Solution

I know that P([tex]\overline{A}[/tex]) = 1 - P(A) = .4

However, I'm not sure how to use the information given to check for independence. The professor says the solution should be very brief, but it's not coming to me.

Thinking on it a little more and looking it up online, it would seem that if P(A|B) = P(A) means A and B are independent, but P([tex]\overline{A}[/tex]) != P(A), then A and B are dependent. But I'm not sure if this logic is correct.

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