# A survey revealed that 44% of people are entertained by reading books, 46% are entertained by watching TV, and 10% are entertained by both books and TV. What is the probability that a person will be entertained by either books or TV?

Apr 12, 2017

$\frac{8}{10} = \frac{4}{5} = .8$

#### Explanation:

Let total surveyed people be $x$.
We are given that 10% $i . e . \frac{10 x}{100}$ people are
entertained by both TV and books.

Since 44% $i . e . \frac{44 x}{100}$ people are entertained by books.
$\therefore$ the number of people entertained ONLY by books is given by:-

(number of people entertained by books)$-$ (number of people entertained by BOTH books and TV)
$= \frac{44 x}{100} - \frac{10 x}{100} = \frac{34 x}{100}$

Similarly,

Since 46% $i . e . \frac{46 x}{100}$ people are entertained by books.
$\therefore$ the number of people entertained ONLY by TV is given by:-

(number of people entertained by TV)$-$ (number of people entertained by BOTH books and TV)
$= \frac{46 x}{100} - \frac{10 x}{100} = \frac{36 x}{100}$

$\therefore$ number of people entertained by EITHER books or TV:-
$=$(number of people entertained ONLY by books) $+$ ( number of people entertained ONLY by TV ) $+$ (People entertained by both TV and books )

$= \frac{34 x}{100} + \frac{36 x}{100} + \frac{10 x}{100} = \frac{80 x}{100}$

$h e n c e ,$ probability that a person will be entertained by either books or TV $=$
(number of people entertained by EITHER books or TV)$/$(total number of people surveyed)

$= \frac{\frac{80 x}{100}}{x} = \frac{8}{10} = 0.8$

Apr 12, 2017

$P$(books or TV) =$\frac{4}{5}$

#### Explanation:

The numbers that are given only tell us about the people who are entertained by books and TV only, but not about other forms of entertainment.

The 44% of people who read includes the 10% who read and watch TV. Therefore we can deduce that 34% of the people are entertained by ONLY books.

In the same way, the people who ONLY watch TV make up 46%-10% =36%

Now we have the information that of people surveyed:

Only books = 34%
Only TV = 36%
Books and TV = 10%

This makes up 34%+36%+10% =80% of people surveyed.

There are therefore 20% who have other forms of entertainment.

The probability that a person is entertained by books or TV :

$P = \frac{80}{100} = \frac{4}{5}$

Apr 13, 2017

 4/5=80%.

#### Explanation:

Let, $B =$ the Event that a person is entertained by reading Books,

$T =$ the event that a person is entertained by watching TV.

Then, $B \cup T =$ the event taht a person is entertained by either

books or TV; and,

$B \cap T =$ the event taht a person is entertained by both the means.

By what is given, we have,

P(B)=44/100, P(T)=46/100, & P(BnnT)=10/100.

$\therefore \text{ The Reqd. Prob=} P \left(B \cup T\right) = P \left(B\right) + P \left(T\right) - P \left(B \cap T\right) ,$

=(44+46-10)/100=80/100=4/5=80%.

Enjoy Maths.!