Compute Probabilities Using the General Multiplication Rule
-If $\mathrm { P } ( \mathrm { A } ) = 0.45 , \mathrm { P } ( \mathrm { B } ) = 0.25$, and $\mathrm { P } ( \mathrm { B } \mid \mathrm { A } ) = 0.45$, are $\mathrm { A }$ and $\mathrm { B }$ independent?
A) no
B) yes
C) cannot determine

Question

Quizplus · Accepted Answer

Two events A and B are independent if $P(A \cap B) = P(A) \cdot P(B)$. Given $P(A) = 0.45$, $P(B) = 0.25$, and $P(B|A) = 0.45$, we can compute $P(A \cap B) = P(A) \cdot P(B|A) = 0.45 \cdot 0.45 = 0.2025$. Since $P(A) \cdot P(B) = 0.45 \cdot 0.25 = 0.1125 \neq P(A \cap B)$, A and B are not independent.

Compute Probabilities Using the General Multiplication Rule -If P(A)=0.45,P(B)=0.25\mathrm { P } ( \mathrm { A } ) = 0.45 , \mathrm { P } ( \mathrm { B } ) = 0.25P(A)=0.45,P(B)=0.25

Compute Probabilities Using the General Multiplication Rule
-If $\mathrm { P } ( \mathrm { A } ) = 0.45 , \mathrm { P } ( \mathrm { B } ) = 0.25$