Edit Problem


D unions intersections and complements
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Easy


Suppose $A$ and $B$ are disjoint with $P(A)=0.3$ and $P(B)=0.5$. What is $P(A'\cap B')$?

Answer:

$0.2$

Solution:

\[\begin{align}P(A'\cap B')&=P((A\cup B)'),\text{ De Morgan's law}\\
&=1-P(A\cup B),\text{ complement rule }\\
&=1-[P(A)+P(B)-P(A\cap B)],\text{ addition rule}\\
&=1-[P(A)+P(B)-P(\emptyset)],\text{ given disjoint}\\
&=1-[0.3+0.5-0]\\
&=0.2.\end{align}
\]