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The probability of happening at least one of the events $A$ and $B$ is 0.6. If the events $A$ and $B$ happens simultaneously with the probability 0.2, then $P (\bar{A}) + P (\bar{B}) = ?$

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1.2

1.4

0.8

0.4

answer is C.

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Detailed Solution

We are given that $P (A \cup B) = 0.6$ and $P (A \cap B) = 0.2$

We know that if $A$ and $B$ are any two events, then

$\begin{array}{l} P (A \cup B) = P (A) + P (B) - P (A \cap B) \\ 0.6 = 1 - P (\bar{A}) + 1 - P (\bar{B}) - 0.2 \end{array}$

$\Rightarrow P (\overline{A}) + P (\overline{B}) = 2 - 0.8 = 1.2$

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