Discussion Forum

If two events , E₁ ,E₂ are such that  

$P(E_{1}\cup E_{2})=\frac{5}{8},P(\overline{E_{1}})=\frac{3}{4}, P(E_{2})=\frac{1}{2} $  then $E_{1}$  and $E_{2}$  are

Answer:

Explanation:

Given, 

$P(E_{1}\cup E_{2})=\frac{5}{8},P(\overline{E_{1}})=\frac{3}{4}, P(E_{2})=\frac{1}{2} $ 

$P(E_{1}\cap {E}_{2})=P(E_{1})+P(E_{2})-P(E_{1}\cup E_{2})$

$P(E_{1}\cap {E}_{2})=\frac{1}{4}+\frac{1}{2}-\frac{5}{8}$

$P(E_{1}\cap {E}_{2})=\frac{1}{8}$

  $P(E_{1}\cap {E}_{2})=P(E_{1})\times P(E_{2})=\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}$

$\therefore$     $E_{1}   and E_{2}$   are independent events