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  • Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E | F)–P(F | E) equals A. 2/7 B. 3/25 C. 1/70 D. 1/7

Two events E and F are independent. If P(E) = 0.3, P(E ∪ F) = 0.5, then P(E | F)–P(F | E) equals
A. 2/7
B. 3/25
C. 1/70
D. 1/7

Answers (1)

Given-

P(E) = 0.3, P(E ∪ F) = 0.5

Also, E and F are independent, therefore,

P (E ∩ F)=P(E).P(F)

As we know , P(E ∪ F)=P(E)+P(F)- P(E ∩ F)
P(E ∪ F)=P(E)+P(F)- [P(E) P(F)]

\\ 0.5=0.3+P(F)-0.3 P(F) \\ 0.5-0.3=(1-0.3) P(F) \\ P(F)=\frac{2}{7}

\\ \\ P(E \mid F)-P(F \mid E)=\frac{P(E \cap F)}{P(F)}-\frac{P(F \cap E)}{P(E)} \\ P(E \mid F)-P(F \mid E)=\frac{P(E \cap F) \cdot[P(E)-P(F)]}{P(E \cap F)} \\ P(E \mid F)-P(F \mid E)=P(E)-P(F) \\ P(F \mid F)-P(F \mid E)=\frac{3}{10} -\frac{2}{7}= \frac{21-20}{70} =\frac{1}{70}

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