Question

The events E and F are given to be independent. Find P(F) if it is given that P(E) = 0.35 and P(E ∪ F) = 0.60.

Solution

Here, P(E) = 0.35, $straight P left parenthesis straight E space union space straight F right parenthesis space equals space 0.60$
Now, $straight P left parenthesis straight E union straight F right parenthesis space equals space straight P left parenthesis straight E right parenthesis space plus space straight P left parenthesis straight F right parenthesis space minus space straight P left parenthesis straight E space intersection thin space straight F right parenthesis$
$rightwards double arrow space space space straight P left parenthesis straight E union straight F right parenthesis space equals space straight P left parenthesis straight E right parenthesis space plus space straight P left parenthesis straight F right parenthesis space minus space straight P left parenthesis straight E right parenthesis thin space straight P left parenthesis straight F right parenthesis space space space left square bracket because space straight E space and space straight F space are space independent right square bracket rightwards double arrow space 0.60 space equals space 0.35 space plus space straight P left parenthesis straight F right parenthesis space minus space left parenthesis 0.35 right parenthesis thin space straight P left parenthesis straight F right parenthesis rightwards double arrow space space left parenthesis 1 minus 0.35 right parenthesis thin space straight P left parenthesis straight F right parenthesis space equals space 0.60 minus 0.35 rightwards double arrow space space space space 0.65 space straight P left parenthesis straight F right parenthesis space equals space 0.25 rightwards double arrow space space space space straight P left parenthesis straight F right parenthesis space equals space fraction numerator 0.25 over denominator 0.65 end fraction space equals 25 over 65 equals 5 over 13.$

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Probability

The events E and F are given to be independent. Find P(F) if it is given that P(E) = 0.35 and P(E ∪ F) = 0.60.

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