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Consider two events $E_1$ and $E_2$ such that probability of $E_1$, $P_r[E_1]=\frac{1}{2}$, probability of $E_2$, $P_r[E_{2}]=\frac{1}{3}$, and probability of $E_1$, and $E_2$, $P_r[E_1 \: and \: E_2] = \frac{1}{5}$. Which of the following statements is/are true?

  1. $P_r[E_1\: \text{or} \:E_2] \text{ is } \frac{2}{3}$

  2. Events $E_1$ and $E_2$ are independent

  3. Events $E_1$ and $E_2$ are not independent

  4. $P_r \left[{E_1}\mid{E_2} \right] = \frac{4}{5}$

asked in Probability by Veteran (59.5k points)
edited by | 593 views

1 Answer

+9 votes
Best answer
Answer - $C$

If events $E_1$ and $E_2$ are independent then $P[E_1$ and $E_2]$ = $P[E_1]\times P[E_2]$ which is not the case here.
answered by Loyal (9k points)
edited by

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