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Problem 12. If P ( A ∣ B ) > P ( A ) \mathrm{P}(\mathrm{A} \mid \mathrm{B})>\mathrm{P}(\mathrm{A}) P ( A ∣ B ) > P ( A ) P ( B ∣ A ) < P ( B ) \mathrm{P}(\mathrm{B} \mid \mathrm{A})<\mathrm{P}(\mathrm{B}) P ( B ∣ A ) < P ( B ) P ( A ∩ B ) < P ( A ) ⋅ P ( B ) \mathrm{P}(\mathrm{A} \cap \mathrm{B})<\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) P ( A ∩ B ) < P ( A ) ⋅ P ( B ) P ( B ∣ A ) > P ( B ) \mathrm{P}(\mathrm{B} \mid \mathrm{A})>\mathrm{P}(\mathrm{B}) P ( B ∣ A ) > P ( B ) P ( B ∣ A ) = P ( B ) \mathrm{P}(\mathrm{B} \mid \mathrm{A})=\mathrm{P}(\mathrm{B}) P ( B ∣ A ) = P ( B ) P ( B ∣ A ) < P ( B ) \mathrm{P}(\mathrm{B} \mid \mathrm{A})<\mathrm{P}(\mathrm{B}) P ( B ∣ A ) < P ( B ) P ( A ∩ B ) < P ( A ) ⋅ P ( B ) \mathrm{P}(\mathrm{A} \cap \mathrm{B})<\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{B}) P ( A ∩ B ) < P ( A ) ⋅ P ( B ) P ( B ∣ A ) > P ( B ) \mathrm{P}(\mathrm{B} \mid \mathrm{A})>\mathrm{P}(\mathrm{B}) P ( B ∣ A ) > P ( B ) P ( B ∣ A ) = P ( B ) \mathrm{P}(\mathrm{B} \mid \mathrm{A})=\mathrm{P}(\mathrm{B}) P ( B ∣ A ) = P ( B ) Browse the problem library