TDSM 2.5
From The Data Science Design Manual Wikia
Using Venn diagram we have:
[math]P(\bar{A} \cap B) = P(B) - P(A \cap B)[/math]
[math]A[/math] and [math]B[/math] are independent so:
[math]P(\bar{A} \cap B) = P(B) - P(A)P(B) = P(B)\left( 1-P(A) \right) = P(B) P(\bar{A}) [/math]
Hence, [math]\bar{A}[/math] and [math]B[/math] are independent.
