Question

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?

Answer 1

`8/10 = 4/5 = .8`

Explanation:

Let total surveyed people be `x`.
We are given that `10%` `i.e. (10x)/100` people are
entertained by both TV and books.

Since `44%` `i.e. (44x)/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`)`
`= (44x)/100 - (10x)/100 = (34x)/100`

Similarly,

Since `46%` `i.e. (46x)/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`)`
`= (46x)/100 - (10x)/100 = (36x)/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 `)`

`= (34x)/100 + (36x)/100 + (10x)/100 = (80x)/100`

`hence,` 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)

`= ((80x)/100)/x = 8/10 = 0.8`

Answer 2

`P`(books or TV) =`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= 80/100 = 4/5`

Answer 3

`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, `BuuT=` the event taht a person is entertained by either

books or TV; and,

`BnnT=` 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.`

`:." The Reqd. Prob="P(BuuT)=P(B)+P(T)-P(BnnT),`

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

Enjoy Maths.!