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Independent Events

If E and E2 a...

Question

If E and $E_{2}$ are independent even, write the value of $P (E_{1} \cup E_{2}) \cap (¯ ¯¯ ¯ E \cap {¯ ¯¯ ¯ E}_{2})$ .

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Solution

$P {(E_{1} \cup E_{2}) \cap ({¯ ¯¯ ¯ E}_{1} \cap {¯ ¯¯ ¯ E}_{2})}$

$= {E_{1} \cap {¯ ¯¯ ¯ E}_{1} \cap {¯ ¯¯ ¯ E}_{2}} \cup {E_{2} \cap ({¯ ¯¯ ¯ E}_{1} \cap {¯ ¯¯ ¯ E}_{2})}$

$= P (ϕ \cup ϕ) = 0$

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