Suppose That an Experiment Has Five Sample Points $E _ { 1 } , E _ { 2 } , E _ { 3 } , E _ { 4 } , E _ { 5 }$

Essay

Suppose that an experiment has five sample points, $E _ { 1 } , E _ { 2 } , E _ { 3 } , E _ { 4 } , E _ { 5 }$ , and that $P \left( E _ { 1 } \right) = .2$ , $P \left( E _ { 2 } \right) = .3 , P \left( E _ { 3 } \right) = .1 , P \left( E _ { 4 } \right) = .1$ , and $P \left( E _ { 5 } \right) = .3$ . If the events $A$ and $B$ are defined as $A = \left\{ E _ { 1 } , E _ { 2 } , E _ { 3 } \right\}$ and $B = \left\{ E _ { 2 } , E _ { 3 } , E _ { 4 } \right\}$ find $P ( A \cap B )$ .