Geometrical Probability

Geometry Level 5

\(ABCDE\) is a convex pentagon with \(\overrightarrow { AB } =2\overrightarrow { DC } \) and \( 3\overrightarrow { AE } =\overrightarrow { BC } \). the diagonals \(AD \) and \(BE\) meet at \(F\).

If \(P(E_{1})=|\frac { \overrightarrow { AF } }{ \overrightarrow { DF } } |,~P(E_{2})=|\frac { \overrightarrow { EF } }{ \overrightarrow { BF } } | \) , where \(E_{1},E_{2},E_{3}\) are mutually exclusive and exhaustive events of an experiment then \(P(E_{3})\) is

Note that \(P(E_{i})\) denotes probability of event \(E_{i}\)

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