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Consider two events \mathrm{E_1 \: and \: E_2} sucn that P\left(E_1\right)=\frac{1}{2}, P\left(E_2\right)=\frac{1}{3} \: and \: P\left(E_1 \cap E_2\right)=\frac{1}{5}.
Which of the following statements is true?

Option: 1

\mathrm {P\left(E_1 \cup E_2\right)=\frac{2}{3}}


Option: 2

\mathrm{E_1 and E_2} are independent


Option: 3

\mathrm{E_1 and E_2} are not independent


Option: 4

\mathrm{P\left(E_1 / E_2\right)=4 / 5}


Answers (1)

best_answer

Option a is wrong
\mathrm{\because \quad P\left(E_1 \cup E_2\right)=\frac{1}{2}+\frac{1}{3}=\frac{19}{30} \neq \frac{2}{3}}

Option b is wrong

\mathrm{ \because \quad P\left(E_1 \cap E_2\right) \neq P\left(E_1\right) P\left(E_2\right) }
Option is (d) is wrong

\mathrm{ \because \quad P\left(E_1 / E_2\right)=\frac{P\left(E_1 \cap E_2\right)}{P\left(E_2\right)}=\frac{\frac{1}{5}}{\frac{1}{3}}=\frac{3}{5} \neq \frac{4}{5} }

Hence option 3 is correct.
 

Posted by

Ritika Jonwal

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