The probability that least one of the events $E_1$ and occurs is 0.6. If the simultaneous occurrence of…

The probability that least one of the events $E_1$ and occurs is 0.6. If the simultaneous occurrence of $E_1$ and $E_2$ is 0.2 , $\mathrm{P}\left(\mathrm{E}_1{ }^{\prime}\right)+\mathrm{P}\left(\mathrm{E}_2^{\prime}\right)=$
  1. 0.4
  2. 1.6
  3. 1.2
  4. 0.8

Solution

$\begin{aligned} & P\left(E_1 \cup E_2\right)=P\left(E_1\right)+P\left(E_2\right)-P\left(E_1 \cap E_2\right) \\ & \therefore 0.6=\left[1-P\left(E_1{ }^{\prime}\right)+1-P\left(E_2{ }^{\prime}\right)-P\left(E_1 \cap E_2\right)\right] \\ & P\left(E_1{ }^{\prime}\right)+P\left(E_2{ }^{\prime}\right)=2-0.2-0.6=1.2\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 2)

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