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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

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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 Select the correct answer from above options

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Given, P(E) = 0.3, P(E ∪ F) = 0.5 Also, E and F are independent, then P (E ∩ F)=P(E).P(F) 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)-0.3P(F) 0.5-0.3 = (1- 0.3) P(F) P(F) = (0.5 -0.3)/0.7 P(F) = 2/7 Since P(E|F)-P(F|E) P(E|F)-P(F|E) = 1/70

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