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Events E and F are independent. Given that P(E) = 0.3 and P(E ∪ F) = 0.5, find the value of P(E|F) - P(F|E).

1. 2/7
2. 3/35
3. 1/70
4. 1/7

Correct answer: 1/70

Solution

P(EuF)=P(E)+P(F)-P(E)P(F)=0.5 => 0.3+0.7P(F)=0.5 => P(F)=2/7. With independence P(E|F)=P(E)=3/10 and P(F|E)=P(F)=2/7, so difference = 3/10 - 2/7 = 1/70.

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