Question

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 any one or both kinds of sets ?

Answer 1

Let $E_1$ be the event that family own colour television set and $E_2$ be

the event that family owns a black and white television set.

it is given that, $P\left(E_1\right)=0.87$

$P\left(E_2\right)=0.36$

and P$(E_1\cap E_2)=0.30$

We have to find probability that a family owns either anyone or both

kind of sets i.e., $P(E_1\cup E_2)$

Now, P$P(E_1\cup E_2)=P\left(E_1\right)+P\left(E_2\right)-P(E_1\cap E_2)$ [by addition theorem]

=0.87+0.36-0.30=0.93