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# In a large metropolitan area ,the probabilities are 0.87,0.36,0.30 that a family (randomly chosen for a sample survey) owns a colour television set,a black and white television set,or both kinds of sets.What is the probability that a family owns either anyone or both kinds of sets?

$\begin{array}{1 1}(A)\;0.73\\(B)\;0.93\\(C)\;0.63\\(D)\;0.43\end{array}$

Toolbox:
• $P(A \cup B)=P(A)+P(B)-P(A\cap B)$
Step 1:
Probability that a family owns a colour television P(A)=0.87
Probability that a family owns a black & white P(B)=0.36
Probability that a family owns both P($A \cap B$)=0.30
Probability that a family owns either anyone or both $P(A \cup B)$=?
Step 2:
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$\Rightarrow 0.87+0.36-0.30$
$\Rightarrow 0.93$
Hence (B) is the correct answer.