Geometrical Probability

Geometry Level 4

$$ABCDE$$ 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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