Statistics Examples

P (A) = 0.5

$P (A) = 0.5$ ,

P (B) = 0.75

$P (B) = 0.75$ ,

P (B g i v e n A) = 0.53

$P (B g i v e n A) = 0.53$

Step 1

Two events are independent events when the occurrence of one does not affect the probability of the other.

P (A | B) = P (A)

$P (A | B) = P (A)$ and

P (B | A) = P (B)

$P (B | A) = P (B)$ .

P (A | B) = P (A)

$P (A | B) = P (A)$

P (B | A) = P (B)

$P (B | A) = P (B)$

Step 2

P (B | A)

$P (B | A)$ should equal to

P (B)

$P (B)$ because the occurrence of

A

$A$ should not effect the probability of

B

$B$ for independent events

A

$A$ and

B

$B$ . In this case,

P (B | A) \neq P (B)

$P (B | A) \neq P (B)$ , which means that

A

$A$ and

B

$B$ are dependent events.

A and B are dependent events

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